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service. Promotion The insurance company advertises logo aggressively. The company uses different events to promote utilizes my personal contact (phone, email, mail…) to inform updated services. The company in person to pursue to deliver agents have sufficient knowledge about company products. The call-center is available 24x7 to handle customer queries. The employees are friendly, polite, and service minded: they ensure your needs are met. There is an island -wide network of assessors, and their response time is less. Primary data is gathered through a cross -sectional survey method which allows to collect population in a timely and cost -effective manner. A Likert scale with endpoints/ being strongly agree and strongly disagree. Measuring sample profile, testing the goodness of the data and testing hypothesis were the main three steps involved in data analysis. Sample profile was measured using the frequently analysis. The reliability and validity of the measurement items were administered to test the goodness of data. In order to test hypotheses, multiple regression analysis was used. Multiple regression analysis was used to determine whether product, price, promotion, and distribution network influence the customer purchase inten tion towards motor insurance in Sri Lanka. The statistical package for social sciences (SPSS) software version 21.0 was used. Findings Out of 446 distributed, 412 questionnaires were taken to conduct the statistical analysis of the study, thus indicating 92 percent of response rate. In demographic factors, 283 responses were from male customers (68.7%) and 129 responses were from female customers. (31.3%). 69 customers (16.7%) were between the age of 18 – 30 years while Weerakkody M. & Nissanka K. AJMM 2023, Vol ( 3), Issue (2), 59-79 68 104 customers (25.2%) and 239 customers (58.1%) were from the age categories of 30 – 45 years and 45 – 60 years respectively. 49 respondents (11.9%) owned motor -bicycles and 24 (5.8%) three -wheeler owners, 313 (76.0%) motor -car owners were also there in the list while 26 customers (6.3%) claimed to be using other types of vehicles. When we discuss about the type of cover, 269 (65.3%) have obtained 3rd party insurance cover where only 143 customers (34.7%) are comprehensive insurance cover users. 52 customer s (12.6%) pay less than Rs. 10,000 annual premium, 49 customers (11.9%) pay between Rs. 10,000 – 25,000, 69 customers (16.7%) pay between Rs. 25,000 – 50,000 whereas, a majority of 211 (51.2%) are paying in between Rs. 50,000 – 100,000 for their annual pre mium. 31 motor insurance policy holders (7.5%) who pay between Rs. 100,000 – 200,000 have also contributed to this survey. Out of the respondents, 113 (27.4%) have been with their respective insurance provider for a period of 1 -5 years. 56 customers (13.6%) are new vehicle owners with less than 1 year duration with a company whereas, 154 (37.4%) and 89 customers (21.6%) have been with their companies for periods of 5 – 10
-5 years. 56 customers (13.6%) are new vehicle owners with less than 1 year duration with a company whereas, 154 (37.4%) and 89 customers (21.6%) have been with their companies for periods of 5 – 10 years and more than 10 years respectively. Measurement Adequacy The sampling adequacy of each variable was measured using the KMO (Kaiser Meyer Olkin) and Bartlett’s Test. These tests measure the suitability of the data collected for each variable. Kurniawan Purnomo (2017) explained that the KMO Measure of Sampling Adequacy should be at least more than 0.5 and the significance value should be less 0.05 in order to ensure the sampling adequacy of each variable (Table 2). A Reliability Analysis was done to ensure the internal consistency of each construct. The Cronbach's Alpha values of each variable will be taken into consideration. Table 2 Assessment of adequacy of measurement Variable No. of Items KM measure Bartlett’s Test of Sphericity AVE Factor Loading Cronbach ’s alpha Product 5 0.818 1150.844 0.71443 Component 1 PD1 0.828 PD2 0.910 PD3 0.833 PD4 0.815 PD5 0.837 0.898 Price 4 0.671 362.000 0.54902 Component 1 PR1 0.746 PR2 0.806 PR3 0.843 PR4 0.855 0.701 Weerakkody M. & Nissanka K. AJMM 2023, Vol ( 3), Issue (2), 59-79 69 Promotion 4 0.740 652.387 0.67849 Component 1 PM1 0.760 PM2 0.911 PM3 0.866 PM4 0.746 0.833 Distribution Network 6 0.870 844.284 0.66875 Component 1 DN1 0.786 DN2 0.878 DN4 0.831 DN5 0.823 DN6 0.766 0.873 Customer Purchase Intention 7 0.788 942.556 0.65129 Component 1 CPI1 0.757 CPI3 0.780 CPI4 0.812 CPI6 0.663 CPI7 0.792 0.825 Table 3 shows that Insurance product recorded the highest mean value. Promotion factor recorded the second highest mean value. Consumer Buying Intention was close to 3.50 which showcases that consumer behaviour in Sri Lanka varies moderately. Bas ed on the correlation values, there were statistically significant correlations among Promotion, Insurance Product, Insurance Premium , Distribution Network and Customer Buying Intention in Sri Lanka. The correlation of these variables are said to b e significant as the given significant value of all the variables are less than 0.01 level (Morel & Kwakye, 2012). Further, none of the correlation coefficient was above 0.85, indicating the absence of multicollinearity in the variabl
What Should A Car Insurance company focus on?Ziwen Liao†Xinxin Zhong‡Di Ma§April, 2024AbstractFollowing the pandemic’s economic impact, auto insurance companies require recovery.To assist companies in understanding their customers better and creating successful strategies,relevant data was collected. This data revealed correlations between customers’ lifetime valueand 24 influencing factors. Out of these factors, nine were selected as the primary focus ofthe research. It is hypothesized that income, vehicle class, and driving location are likely to bethe most influential factors in customers’ lifetime value. To validate this hypothesis, we willuse R Studio software to analyze whether a significant correlation exists between customers’lifetime value and these nine independent variables. The analysis methods include the t-test,simple regression model, multiple linear regression model, and logistic regression model. Thefindings suggest that monthly premiums, marital status, vehicle class, income, coverage, andlocation may contribute to customers’ lifetime value.Key words: Auto-insurance companies, Marketing strategies, CLV (customers’ lifetime value)1 IntroductionUnder the shadow of the pandemic, Americans worked from home instead of commuting towork. Patrick T. Fallon (2023) stated that employees save time, but auto insurance firms suffersignificant losses as a result. According to an S&P Global Market Intelligence investigation inEngineering Department (Industrial Engineering), California State Polytechnic University, Pomona, Los Angeles,91766, USA†Corresponding author. Email: zliao@cpp.edu‡Engineering Department (Information Management of Business), University College London, London, WC1E6BT, UK§Department of Mathematics, University of California of San Diego, La Jolla, 92093, USA 2023, the private vehicle insurance market in the United States experienced its poorest underwritingloss in more than 20 years in 2022.To achieve effective recovery, insurance companies must create efficient strategies that assisttheir executives in establishing organizational objectives, providing businesses with a competitiveedge, and allocating resources. Since the insurance industry is a service sector, these strategiesshould also address how businesses should interact with various types of clients. Insurance firmsshould be aware of customers’ profitability; in other words, they must understand their prioritiesin order to develop and justify appropriate marketing initiatives.To determine the marketing initiatives for an individual customer, there is a useful value calledlifetime value. In an article written by Caldwell (2022), it is shown that Customer Lifetime Value(CLV) is a statistic used to determine the amount of money a company can expect to earn froma typical customer throughout the duration of their relationship with the company. Kumar, Ra-mani, and Bohling (2004) explained that businesses intend to calculate the lifetime value of eachcustomer and use this
throughout the duration of their relationship with the company. Kumar, Ra-mani, and Bohling (2004) explained that businesses intend to calculate the lifetime value of eachcustomer and use this data to develop distinctive marketing campaigns tailored to each individual.Therefore, the first research question pertains to the traits of customers with higher lifetime values,while the second study question involves finding out how these characteristics might impact thelifetime value of consumers.RQ1: Which traits of auto insurance customers would affect the lifetime value?RQ2: Through what mechanisms do these traits affect the lifetime value?According to the research questions, we formulated hypotheses based on the definition of CLVand other materials:H1: There is a relationship between the customer’s driving location and their lifetime value.The more risky the location, the lower the lifetime value.The risk of driving is one of the factors presumptively associated with lifetime value. Accord-ing to SAS (2018), CLV takes into account the difference between total customer revenues andtotal customer expenses throughout the entire business relationship. Claims represent the coststhat clients of auto insurance companies might incur. Therefore, assuming that the premium re-mains at the same level, the lifetime value of the customer reduces when there is a higher potentialfor claims while driving. This suggests that there is a negative correlation between lifetime value and driving risks.Driving in a rural area is significantly riskier than driving in an urban area, according to a studyby psychologists Ilan Shrira of Arkansas Tech University and Kenji Noguchi of the University ofSouthern Mississippi (2016). This study demonstrates how closely the location of driving affectsthe risks associated with driving. Hence, there is a strong likelihood that the driving location isrelated to the lifetime value.H2: There is a positive relationship between income and lifetime value. The higher the cus-tomer’s income, the higher their lifetime value.In line with the SAS definition of CLV , income can also influence lifetime value. When in-come increases, disposable income (net income) also increases correspondingly. Assuming othervariables remain constant, the proportion of income that can be spent on insurance also increases,leading to a higher lifetime value for the customer.H3: The class of the vehicle influences the lifetime value. The higher the vehicle’s class, thehigher the customer’s lifetime value.It’s a well-known fact that a vehicle’s value increases with its level of luxury. After examiningthree different websites providing car insurance quotes, such as comparethemarket, we found thatthe estimated automobile value is a crucial factor. As the value of the car increases, the predictedpremium also increases. When the risk of needing to make claims is reduced, the lifetime value ofthe client increases due to the higher premium that their car commands. To support
the predictedpremium also increases. When the risk of needing to make claims is reduced, the lifetime value ofthe client increases due to the higher premium that their car commands. To support our hypothesisand identify more potential variables related to lifetime value, we analyzed a dataset containinginformation for 9135 auto insurance customers with nine variables.2 MethodologyThis study utilized data from "Kaggle Jenks Natural Breaks and K-means Clustering" (2022)to investigate the characteristics of clients exhibiting a higher lifetime value. We examined adataset comprising 9135 auto insurance customers across nine variables, establishing comparisonsbetween each variable and the lifetime value. Subsequently, the researchers sought correlationsbetween each variable and lifetime value, assessing the significance of these associations. Data processing was conducted using R Studio software, employing four statistical models to validatethe significance of our regression model and confirm our hypotheses.Figure 1: The correlation tableAs shown in Figure 1, the final findings suggest a negligible correlation between Lifetime.valueand Income. Notably, a positive correlation emerges with Total.Claim.Amount, with a likewisesignificant positive correlation discernible with Monthly.Premium.Auto. Furthermore, the associ-ations between Lifetime.value and other factor-based variables are visually represented.Then, we show the descriptive statistics for all numerical variables. The results are exhibitedin Table 1.Table 1. descriptive statisticsNumber ofobservationsMean StandarddeviationMaximum MinimumCustomer.Lifetime.Value 9134 8004.94 6870.97 83325.38 1898.01Income 9134 37657.38 30379.90 99981.00 0.00Monthly.Premium.Auto 9134 93.22 34.41 298.00 61.00Total.Claim.Amount 9134 434.09 290.50 2893.24 0.10From the result, the mean value of the lifetime value is 8004.94, this is much lower than themaximum value (83325.38). It means most of the lifetime value of this variable is lower than its mean value. Regarding the "Income" variable, the average income of the customers is 37657.38.The standard deviation (30379.90) is slightly lower than its mean value. This means that the widegap between rich and poor customers. In addition, the average monthly premium paid by thecustomers is 93.22, and the average claim amount made by customers is 434.09.2.1 CovergeIn the context of this research, the interplay between "Coverage" and "Customer.Lifetime.Value"is probed by employing box plot visualizations. Through the use of the "ggplot2" library, the as-cendant trend in Lifetime Value is depicted, progressing from Basic to Extended and culminatingin Premium levels of Coverage. To robustly ascertain the influence of Coverage on Lifetime Value,a t-test is conducted. The dataset is divided into three factions predicated on the Coverage level:Basic, Extended, and Premium. As shown in Figure 2, results from the t-test divulge a statisticallysignificant disparity in Lifetime Value
divided into three factions predicated on the Coverage level:Basic, Extended, and Premium. As shown in Figure 2, results from the t-test divulge a statisticallysignificant disparity in Lifetime Value between both Extended and Basic Coverage, and Premiumand Extended Coverage, with p-values falling below 0.01. This outcome significantly refutes theinitial hypothesis and corroborates that both Extended and Premium Coverage tiers exhibit higherLifetime Values in comparison to Basic Coverage.Figure 2: Plot for Customer Lifetime. Value & Coverage The other quantitative variables are analyzed in a similar way.2.2 GenderIn the context of this investigation, the prospective association between "Gender" and "Cus-tomer Lifetime Value" is scrutinized by leveraging the "ggplot2" library, through box plot visual-izations. The diagram elucidates the distribution of "Customer Lifetime Value" across two genderclassifications, female (F) and male (M). As shown in Figure 3, from an initial visual inspection,gender does not appear to exert a substantial influence on variations in Lifetime Value. To sub-stantiate this preliminary observation, a t-test was performed on the Lifetime Value of the femaleand male cohorts. The outcomes display a p-value exceeding 0.1, suggesting that the initial hy-pothesis proposing a gender effect on lifetime values is statistically untenable. Consequently, adeduction suggests that gender does not appear to be linked to fluctuations in lifetime value withinthis dataset.Figure 3: Plot for Customer Lifetime. Value & Gender2.3 Location.CodeIn this study, "ggplot2" box plot is used to elucidate the possible influence of "Location.Code"on "Customer Lifetime Value". The plot demonstrates the dispersion of "Customer Lifetime Value" across distinct Location.Codes, encompassing rural, suburban, and urban areas. As shown in Fig-ure 4, from an initial visual inspection, Location.Code appears to exert minimal effect on the vari-ance in Lifetime Value. To rigorously scrutinize this association, multiple t-tests is implementedto compare lifetime values across the three Location.Code groups. The outcome revealed p-valuesexceeding 0.1 for all tests, signifying insufficient statistical evidence to refute the initial hypothe-sis. Thus, the conclusion is that Location.Code does not exert a significant influence on CustomerLifetime Value within this dataset.Figure 4: Plot for Customer Lifetime. Value & Location. Code2.4 Marital.StatusIn the course of this investigation, the potential impact of "Marital.Status" on "Customer.Lifetime.Value,"is shown utilizing "ggplot2" to generate boxplot visualizations. The plot exhibits the distributionof Lifetime Values across varying Marital Status categories, namely Divorced, Married, and Sin-gle. Upon visual examination, it becomes apparent that "Marital.Status" does not significantlysway variations in Lifetime Values. To perform an exhaustive analysis, multiple t-tests is executed,comparing Lifetime Values among the
it becomes apparent that "Marital.Status" does not significantlysway variations in Lifetime Values. To perform an exhaustive analysis, multiple t-tests is executed,comparing Lifetime Values among the different Marital Status cohorts. As shown in Figure 5, the results of the t-tests offer intriguing insights: the juxtaposition ofDivorced and Married groups returns a p-value surpassing 0.1, suggesting that the original hypoth-esis of a notable disparity is not upheld. However, the comparison between the divorced and singlegroups yields a p-value below 0.05, compelling us to reject the original hypothesis and intimatinga significant discrepancy in Lifetime Values between these groups. Additionally, the comparisonbetween Married and Single groups yields a p-value less than 0.05, once again indicating a signifi-cant difference in Lifetime Values. These findings suggest that Single individuals typically possesslower Lifetime Values compared to those who have been Married at least once. However, no signif-icant difference is observed between the Lifetime Values of the divorced and married groups. Thisunderscores the importance of considering Marital Status as a potential influencer of CustomerLifetime Values within the dataset.Figure 5: Plot for Customer Lifetime. Value & Marital. Status2.5 Sales.ChannelThis study investigates the potential influence of various sales channels (Agent, Branch, CallCenter, and Web) on Customer Lifetime Value (CLV), employing boxplot visualizations con-structed via the ggplot2 library. These visualizations depict the distribution of CLV across thesales channel categories, including Agent, Branch, Call Center, and Web. As shown in Figure 6, the preliminary visual analysis, however, reveals no significant corre-lation between the choice of "Sales.Channel" and the variability in Lifetime Values. This initialobservation necessitates a deeper examination, hence a sequence of t-tests, contrasting the Life-time Values among diverse sales channel groups. Remarkably, the t-tests systematically presentp-values exceeding 0.1 for all pairings, implying insufficient statistical evidence to challenge theprimary assumption. Consequently, it is inferred that the selection of a sales channel has no de-tectable impact on the Customer.Lifetime.Value in this data set.These insights underscore the notion that the type of sales channel, be it Agent, Branch, CallCenter, or Web, does not significantly influence the determination of CLV . It reinforces the premiseof the sales channel’s independence in relation to CLV variability, suggesting that other parametersmay exercise a more pronounced effect in shaping customer behaviors within this dataset’s context.Figure 6: Plot for Customer Lifetime. Value & Sales. Channel2.6 Vehicle.ClassThis investigation explores the effect of vehicle classes (Two-Door Car, Four-Door Car, SportsCar, SUV , Luxury Car, and Luxury SUV) on the CLV , using boxplot visualizations generatedthrough ggplot2.As shown in Figure
explores the effect of vehicle classes (Two-Door Car, Four-Door Car, SportsCar, SUV , Luxury Car, and Luxury SUV) on the CLV , using boxplot visualizations generatedthrough ggplot2.As shown in Figure 7, upon visual inspection, a distinct correlation emerges between vehicle class and CLV variance. To validate this observation, a series of t-tests are executed comparing theCLV among different vehicle classes.The t-tests expose fascinating results: While the comparisons between Two-Door Car, Four-Door Car, and SUV with other vehicle classes manifest p-values greater than 0.1, contrasts betweenTwo-Door Car, Four-Door Car, and classes such as Sports Car, Luxury Car, and Luxury SUV yieldp-values less than 0.01. These results compel the rejection of the initial hypothesis.Conclusively, vehicle class appears to segregate CLV into three distinct tiers: the lowest tiercorrelates with Two-Door Car and Four-Door Car categories, followed by Sports Car and SUV .The highest tier is dominated by Luxury Car and Luxury SUV categories, implying a higher CLVamong customers driving these vehicles. This data highlights the significant role vehicle class playsin analyzing CLV , as various vehicle classes exert diverse effects on customer lifetime values.Figure 7: Plot for Customer Lifetime. Value & Vehicle. ClassUnder T test:In addition to the box plots above, we additionally applied the t-test to determine whetherCustome Lifetime Value is dependent on these variables. The t test results are reported in Table 2.Table 2. T test result Variable Null hypothesis T StatisticCoveragemean(Y\|Basic) = mean(Y\|Extended) −9.75∗∗∗mean(Y\|Extend) = mean(Y\|Premium) −6.49∗∗∗Gender mean(Y\|Male) = mean(Y\|Male) 1.30Location.Codemean(Y\|Rural) = mean(Y\|Suburban) -0.28mean(Y\|Suburban) = mean(Y\|Urban) -0.31mean(Y\|Rural) = mean(Y\|Urban) -0.47Marital.Statusmean(Y\|Divorced) = mean(Y\|Married) 0.77mean(Y\|Divorced) = mean(Y\|Single) 2.27∗∗mean(Y\|Married) = mean(Y\|Single) 2.20∗∗Sales.Channelmean(Y\|Agent) = mean(Y\|Branch) -0.90mean(Y\|Agent) = mean(Y\|Call Center) -0.70mean(Y\|Agent) = mean(Y\|Web) 0.82mean(Y\|Branch) = mean(Y\|Call Center) 0.09mean(Y\|Branch) = mean(Y\|Web) 1.46mean(Y\|Call Center) = mean(Y\|Web) 1.27Vehicle.Classmean(Y\|Two-Door Car) = mean(Y\|Four-Door Car) 0.28mean(Y\|Two-Door Car) = mean(Y\|Sports Car) −10 .13∗∗∗mean(Y\|Two-Door Car) = mean(Y\|SUV) −17 .00∗∗∗mean(Y\|Two-Door Car) = mean(Y\|Luxury Car) −10 .49∗∗∗mean(Y\|Two-Door Car) = mean(Y\|Luxury SUV) −11 .10∗∗∗mean(Y\|Four-Door Car) = mean(Y\|Sports Car) −10 .51∗∗∗mean(Y\|Four-Door Car) = mean(Y\|SUV) −18 .85∗∗∗mean(Y\|Four-Door Car) = mean(Y\|Luxury Car) −10 .58∗∗∗mean(Y\|Four-Door Car) = mean(Y\|Luxury SUV) −11 .19∗∗∗mean(Y\|Sports Car) = mean(Y\|SUV) 0.72mean(Y\|Sports Car) = mean(Y\|Luxury Car) −5.97∗∗∗mean(Y\|Sports Car) = mean(Y\|Luxury SUV) −6.31∗∗∗mean(Y\|SUV) = mean(Y\|Luxury Car) −6.61∗∗∗mean(Y\|SUV) = mean(Y\|Luxury SUV) −7.01∗∗∗mean(Y\|Luxury Car) = mean(Y\|Luxury SUV) -0.05 Note: * represent 10% significance level, ** represent 5% significance level;
= mean(Y\|Luxury Car) −6.61∗∗∗mean(Y\|SUV) = mean(Y\|Luxury SUV) −7.01∗∗∗mean(Y\|Luxury Car) = mean(Y\|Luxury SUV) -0.05 Note: * represent 10% significance level, represent 5% significance level; * represent 1%significance level. Y is the ‘Custome Lifetime Value’. When t statistic > 0, it means thatmean(Y\|situation 1) > mean(Y\|situation 2).In the Table 1 above, when the t statistics is significant, we reject the corresponding null hy-pothesis and then the variable is going to impact the Custome.Lifetime.Value. Here, we findthat the Custome Lifetime Value has nothing to do with variables “Gender”, “Location.Code”,“Sales.Channel”. It depends on “Coverage”, “Marital.Status” and “Vehicle.Class”. In addition,we can get several interesting results. First, people who have a higher degree of Coverage possesshigher lifetime value; Second, people who are married or have been married before have higherlifetime values than those who are single. At last, Vehicle.Class categorizes Lifetime Value intothree classes. "Two-Door Car" and "Four-Door Car" have the lowest lifetime value, followed by"Sports Car" and "SUV", and the highest lifetime value are "Luxury Car" and "Luxury SUV".3 Simple regressionSimple regression analyses were undertaken to elucidate the relationship between CustomerLifetime Value (CLV) and several independent variables. The regression result is shown in Table3.Table 3: Simple regression resultCustomer.Lifetime.Value(1) (2) (3) (4) (5) (6) (7) (8) (9)Coverage(Extended)1,598 .971∗∗∗(158.021)Coverage(Premium)3,704 .897∗∗∗(252.816)Gender(Male)-187.051(143.809)Income0.006∗∗(0.002)Location.Code(Suburban)50.758 (186.557)Location.Code(Urban)110.434(237.656)Marital.Status(Married)-162.272(208.264)Marital.Status(Single)−526 .402∗∗(231.505)Monthly.Premium.Auto79 .130∗∗∗(1.919)Sales.Channel(Branch)162.003(178.802)Sales.Channel(Call Center)142.376(200.817)Sales.Channel(Web)-177.921(221.834)Total.Claim.Amount5.356∗∗∗(0.241)Vehicle.Class(Luxury Car)10 ,421 .620∗∗∗(511.580)Vehicle.Class(LuxurySUV)10 ,491 .270∗∗∗(482.558)Vehicle.Class(Sports Car)4,119 .263∗∗∗(306.681)Vehicle.Class(SUV)3,811 .785∗∗∗(178.495)Vehicle.Class(Two-Door Car)39.304(175.401)Constant7,190 .706∗∗∗8,096 .602∗∗∗7,797 .421∗∗∗7,953 .699∗∗∗8,241 .239∗∗∗628 .500∗∗∗7,957 .709∗∗∗5,679 .933∗∗∗6,631 .727∗∗∗(90.771) (100.670) (114.475) (163.195) (185.655) (190.643) (116.526) (125.919) (94.430)Observations 9,134 9,134 9,134 9,134 9,134 9,134 9,134 9,134 9,134From the Table 3, we can get the following information. The analytical observations revealedthat among the examined variables, Coverage emerged as a significant predictor of the dependentvariable. Conversely, Gender, as an independent variable, demonstrated consistent insignificanceconcerning the CLV . Both Income and Monthly Premium Auto were confirmed as significant pre-dictors, whereas Location Code and Sales Channel failed to achieve any significance in their re-spective regressions. The regression involving Marital Status suggested that
as significant pre-dictors, whereas Location Code and Sales Channel failed to achieve any significance in their re-spective regressions. The regression involving Marital Status suggested that the Single categorywas significantly associated with the dependent variable. Similarly, Vehicle Class was discerned as a significant predictor. In summary, Income, Marital Status, Monthly Premium Auto, and VehicleClass were observed to share significant relationships with CLV , in contrast to Gender, LocationCode, and Sales Channel, which exhibited no such correlations.4 Multiple Linear RegressionA multivariate linear regression was executed to evaluate the collective impact of diverse vari-ables on the Customer Lifetime Value. The result is shown in Table 4.Table 4: Multiple Linear Regression resultCustomer.Lifetime.Value(1) (2) (3) (4) (5) (6)Coverage(Extended)121.491 121.573(249.561) (249.543)Coverage(Premium)179.727 168.693(527.771) (527.686)Gender(Male)-177.346 -185.203 -184.452 -180.969 -196.145(132.859) (132.712) (132.663) (132.626) (132.107)Income0.004 0.005∗0.005∗0.005∗0.006∗∗0.006∗∗(0.003) (0.002) (0.002) (0.002) (0.002) (0.002)Location.Code(Suburban)-69.115(257.762)Location.Code(Urban)185.358(241.095)Marital.Status(Married)-259.392 -248.558 -247.778 -242.889 -237.397 -235.909(191.718) (191.511) (191.443) (191.410) (191.369) (191.379)Marital.Status(Single)−490 .744∗∗−483 .825∗∗−482 .776∗∗−483 .563∗∗−524 .387∗∗−532 .486∗∗(220.046) (218.916) (218.843) (218.821) (216.525) (216.470)Monthly.Premium.Auto70 .588∗∗∗70 .991∗∗∗74 .459∗∗∗74 .526∗∗∗72 .284∗∗∗72 .432∗∗∗(10.026) (9.906) (4.346) (4.345) (3.982) (3.981)Sales.Channel(Branch)184.866 185.077 184.564 (164.222) (164.200) (164.177)Sales.Channel(Call Center)220.589 219.732 217.555(184.439) (184.430) (184.360)Sales.Channel(Web)-126.205 -124.866 -127.474(203.713) (203.687) (203.558)Total.Claim.Amount-0.320 -0.428 -0.433 -0.435(0.468) (0.338) (0.338) (0.338)Vehicle.Class(Luxury Car)1,209.726 1,215.593 759.430 769.504 736.242 705.240(1,386.213) (1,386.148) (735.873) (735.653) (735.227) (734.979)Vehicle.Class(Luxury SUV)1,199.025 1,205.723 752.218 717.400 704.756 671.409(1,373.969) (1,373.930) (719.286) (719.046) (719.005) (718.701)Vehicle.Class(Sports Car)1,083 .182∗∗1,081 .758∗∗928 .901∗∗∗919 .029∗∗∗932 .540∗∗∗922 .018∗∗∗(526.230) (526.210) (349.540) (349.494) (349.349) (349.300)Vehicle.Class(Sports Car)871 .506∗876 .100∗726 .432∗∗∗730 .618∗∗∗732 .586∗∗∗724 .670∗∗∗(456.911) (456.852) (244.430) (244.409) (244.413) (244.371)Vehicle.Class(Two-Door Car)76.736 74.752 73.677 82.432 80.711 75.375(172.418) (172.407) (172.370) (172.311) (172.312) (172.286)Constant1,381 .393∗1,347 .179∗1,134 .658∗∗∗1,199 .153∗∗∗1,188 .087∗∗∗1,083 .659∗∗∗(726.348) (693.978) (386.883) (376.936) (376.852) (370.255)Observations 9,134 9,134 9,134 9,134 9,134 9,134Adjusted R20.159 0.159 0.159 0.159 0.159 0.159From the Table 4, the preliminary regression embraced all variables, yielding an AdjustedR-squared value of 0.159. This metric
9,134 9,134 9,134 9,134Adjusted R20.159 0.159 0.159 0.159 0.159 0.159From the Table 4, the preliminary regression embraced all variables, yielding an AdjustedR-squared value of 0.159. This metric offers an estimate of the model’s capability to replicateobserved outcomes, where a value ranging from 0 to 1 denotes the fraction of total variation ’ex-plained’ by the model.To further optimize the model, a stepwise regression technique was employed. This proce-dure entails the fitting of regression models by systematically adding or eliminating predictorsbased on their statistical significance. Firstly, the variable "Location.Code", possessing the highestp-value of 0.7886, was excluded from the model. This action was underpinned by the assump-tion that an elevated p-value signifies a potential lack of significance in the variable, particularlywithin the context of the other variables. Secondly, following the elimination of "Location.Code", "Coverage" was identified as the variable with the subsequent highest p-value (0.7492). This in-dicated the variable’s prospective insignificance, and thus, it was extricated from the regressionmodel. Thirdly, after the removal of "Coverage", all p-values linked to "Sales Channel" exhibitedinsignificance. Consequently, "Sales Channel" was the ensuing variable to be purged. Fourthly,"Total.Claim.Amount" was determined as an insignificant variable and, hence, was excised fromthe regression equation. Fifthly: "Gender" surfaced as the variable with the highest p-value in theupdated model, hinting that it might not constitute a significant predictor in the presence of othervariables. Thus, it was successively removed.After the stepwise elimination process, the variables retained in the regression model were"Income", "Marital.Status", "Monthly.Premium.Auto", and "Vehicle.Class". These four variableswere suggested to be significant predictors of Customer Lifetime Value within the context of theexisting dataset. This optimized model offers a more parsimonious and potentially comprehensibleinterpretation of the relationship between the predictors and the outcome.5 constructing logistic regressionWithin the analysis, logistic regression is leveraged to predict a binary outcome on the basis ofmultiple predictors. The binary outcome in this scenario signifies whether the Customer LifetimeValue surpasses or falls below its median value.Initial Preprocessing:• The dataset is imported, and a novel variable, "LifeT", is established. This variable is as-signed the value "1" if a customer’s Lifetime Value equals or exceeds the median value, and"0" otherwise.• Two columns, "Customer.Lifetime.Value" and "Customer", are removed from the dataset toevade redundancy and potential multicollinearity.Then, we perform the logistic regression model. The result is reported in Table 5.Univariate Logistic Regression: Prior to progressing with a comprehensive model, each predictor was individually evaluatedagainst the dependent variable "LifeT" to
The result is reported in Table 5.Univariate Logistic Regression: Prior to progressing with a comprehensive model, each predictor was individually evaluatedagainst the dependent variable "LifeT" to comprehend their individual significance. The result isreported in Table 5.Table 5: Univariate Logistic Regression resultLifeT(1) (2) (3) (4) (5) (6) (7) (8) (9)Coverage(Extended)0.894∗∗∗(0.048)Coverage(Premium)1.408∗∗∗(0.084)Gender(Male)0.038(0.042)Income0.000∗(0.000)Location.Code(Suburban)-0.033(0.054)Location.Code(Urban)-0.043(0.069)Marital.Status(Married)-0.021(0.061)Marital.Status(Single)−0.125∗(0.067)Monthly.Premium.Auto0.032∗∗∗(0.001)Sales.Channel(Branch)-0.012(0.052)Sales.Channel(Call Center)-0.021(0.058)Sales.Channel(Web)-0.087(0.065)Total.Claim.Amount0.002∗∗∗(0.0001)Vehicle.Class(Luxury Car)16.914(187.947)Vehicle.Class(Luxury SUV)16.914(176.897)Vehicle.Class(Sports Car)1.177∗∗∗ (0.103)Vehicle.Class(SUV)1.035∗∗∗(0.058)Vehicle.Class(Two-Door Car)-0.002(0.055)Constant−0.385∗∗∗-0.016 -0.048 0.030 0.048 −2.860∗∗∗0.022 −0.673∗∗∗−0.348∗∗∗(0.027) (0.029) (0.033) (0.048) (0.054) (0.090) (0.034) (0.041) (0.030)Observations 9,134 9,134 9,134 9,134 9,134 9,134 9,134 9,134 9,134From the Table 5, we find two interesting conclusions:• "Coverage", "Income", "Marital.Status", "Monthly.Premium.Auto", "Total.Claim.Amount",and "Vehicle.Class" were all identified as significant predictors.• In their individual regressions, "Gender", "Location.Code", and "Sales.Channel" did not dis-play significant impacts.Multiple Logistic Regression:Then, we use a similar way as the multiple OLS regression to perform multiple logistic regres-sion here. The result is shown in Table 6.Table 6: Multiple Logistic Regression resultLifeT(1) (2) (3) (4) (5) (6)Coverage(Extended)0.494∗∗∗0.495∗∗∗0.397∗∗∗0.397∗∗∗0.396∗∗∗0.394∗∗∗(0.096) (0.095) (0.053) (0.053) (0.053) (0.053)Coverage(Premium)0.441∗∗0.441∗∗0.226∗∗0.226∗∗0.226∗∗0.230∗∗(0.198) (0.198) (0.096) (0.096) (0.096) (0.096)Gender(Male)0.053 0.054 0.058 0.058(0.046) (0.046) (0.046) (0.046)Income0.00000 0.00000 0.00000 0.00000 0.00000(0.00000) (0.00000) (0.00000) (0.00000) (0.00000)Location.Code(Suburban)-0.095 -0.093 -0.110 −0.118∗−0.112∗−0.142∗∗ (0.094) (0.094) (0.093) (0.064) (0.064) (0.060)Location.Code(Urban)-0.025 -0.024 -0.035 -0.040 -0.040 -0.041(0.084) (0.084) (0.084) (0.075) (0.075) (0.075)Marital.Status(Married)-0.060 -0.060 -0.059 -0.059 -0.059 -0.058(0.066) (0.066) (0.066) (0.066) (0.066) (0.066)Marital.Status(Single)−0.152∗∗−0.151∗∗−0.149∗−0.150∗∗−0.148∗∗−0.164∗∗(0.076) (0.076) (0.076) (0.075) (0.075) (0.074)Monthly.Premium.Auto0.024∗∗∗0.024∗∗∗0.029∗∗∗0.029∗∗∗0.029∗∗∗0.029∗∗∗(0.004) (0.004) (0.001) (0.001) (0.001) (0.001)Sales.Channel(Branch)-0.015(0.057)Sales.Channel(Call Center)0.002(0.064)Sales.Channel(Web)-0.066(0.071)Total.Claim.Amount-0.0001 -0.0001 -0.00002(0.0002) (0.0002) (0.0002)Vehicle.Class(Luxury Car)13.891 13.887(172.954) (173.026)Vehicle.Class(Luxury SUV)13.809 13.806(162.969) (162.969)Vehicle.Class(Sports
-0.0001 -0.00002(0.0002) (0.0002) (0.0002)Vehicle.Class(Luxury Car)13.891 13.887(172.954) (173.026)Vehicle.Class(Luxury SUV)13.809 13.806(162.969) (162.969)Vehicle.Class(Sports Car)0.224 0.222(0.205) (0.205)Vehicle.Class(SUV)0.111 0.111(0.182) (0.182)Vehicle.Class(Two-Door Car)0.019 0.020(0.058) (0.058)Constant−2.336∗∗∗−2.353∗∗∗−2.693∗∗∗−2.687∗∗∗−2.663∗∗∗−2.595∗∗∗(0.296) (0.294) (0.137) (0.126) (0.125) (0.114)Observations 9,134 9,134 9,134 9,134 9,134 9,134From the Table 6, we can get 7 interesting results. 1. Commencing with a comprehensive logistic regression inclusive of all predictors, the derivedmodel was statistically significant. The ensuing stepwise refinement aimed to eradicate po-tentially extraneous predictors.2. Initially, the "Sales.Channel" variable was pruned, ascribed to its highest p-value suggestingthe least substantive predictor among the assemblage.3. Following this, "Vehicle.Class", with a diminished level of significance, was eliminated.4. Subsequently, the "Total.Claim.Amount" was abandoned, thereby streamlining the modelfurther.5. Following it, "Gender" showed the highest p-value and was excluded from the model.6. Ultimately, the "Income" variable, despite its significance in individual regression, mani-fested diminished importance in the multivariate context and was therefore excised.7. After this systematic elimination, the refined model retained "Coverage", "Location.Code","Marital.Status", and "Monthly.Premium.Auto" as its integral variables.6 ResultsThe results concluded from the data analysis indicate that marriage status, monthly premiumamount, and vehicle class are significantly correlated with the lifetime value of auto insurancecustomers in all analysis models. However, income is significant in most models except in logisticregression. As for coverage and location code, they emerge as significant only in the logisticregression. The reasons for these outcomes warrant further research. First and foremost, themonthly premium amount has the highest correlation with lifetime value. This is because customerlifetime value (CLV) is closely related to the value that a customer brings to the organization. Inthe insurance industry, the value the customer provides is the premium. Premium, which is anindicator of customer value, is also included in the traditional formula for calculating CLV , asmentioned by Caldwell (2022): CLV=Customer Value ×Average Customer Lifespan (1)Next, the consistent significance of marital status across models indicates that marital statusplays a crucial role in determining CLV . This could be because marital status might be associatedwith financial stability, purchasing patterns, or risk behavior, which, in turn, affects insurancepremiums or claims. There is also a possibility that this data may be biased and not randomlychosen, as the company investigated may be more focused on young clients.Vehicle class can be a reflection of lifestyle, financial status, and even risky behavior. Moredirectly,
and not randomlychosen, as the company investigated may be more focused on young clients.Vehicle class can be a reflection of lifestyle, financial status, and even risky behavior. Moredirectly, it is an indicator of the value of the vehicle, which can impact insurance quotes, as men-tioned in the introduction. The significant association suggests varying CLVs for different vehiclecategories, possibly due to differences in premiums, claim frequency, or claim amounts.In the majority of models, except for logistic regression, income is considered important be-cause it is linked to other variables. Income is connected to lifetime value when tested on its own.However, the results of logistic regression would be invalid if income and other variables relatedto income were tested alongside lifetime value. Income is a key factor in determining a person’spurchasing power and financial behavior, and variables like vehicle class have a positive link withincome, according to Team, T.I. (2023). The higher the income, the higher the class of car.As for coverage and location code, which only show significance in logistic regression, it’spossible that when modeling the probability of CLV being above or below a median (as is thecase in logistic regression), the type of coverage a customer has and their location become pivotaldeterminants. Perhaps certain coverages or locations are associated with significantly higher orlower lifetime values.In summary, the conducted analysis illuminates how a combination of socio-economic factors(such as marital status and income), product-specif
10.243620.8080.02.20Conditional likelihood based inference onsingle-index models for motor insurance claimseverityCatalina Bolance ´1, Ricardo Cao2and Montserrat Guillen1Abstract Prediction of a traffc accident cost is one of the major problems in motor insurance.To identify the factors that infuence costs is one of the main challenges of actuarialmodelling. Telematics data about individual driving patterns could help calculating theexpected claim severity in motor insurance. We propose using single-index models toassess the marginal effects of covariates on the claim severity conditional distribution.Thus, drivers with a claim cost distribution that has a long tail can be identifed. Theseare risky drivers, who should pay a higher insurance premium and for whom preventa-tive actions can be designed. A new kernel approach to estimate the covariance matrixof coeffcients’ estimator is outlined. Its statistical properties are described and an ap-plication to an innovative data set containing information on driving styles is presented.The method provides good results when the response variable is skewed.MSC: 62G05, 62P20, 91G70. Keywords: covariance matrix of estimator, kernel estimator, marginal effects, telematics covari-ates, right-skewed cost variable. 1.IntroductionWe analyse costs of claims in a motor insurance data set. Because higher costs occurmuch less frequently than lower costs of claims, the dependent variable here is right-skewed. Specifcally, we are interested in modelling the distribution of costs of claimsconditional on the values of covariates that refect driving habits. We focus on the wholeconditional distribution rather than on the conditional expectation to measure the infu-ence of covariates on different quantiles, specifcally on the costly claims, i.e., the right1Department of Econometrics, RISKcenter-IREA, Universitat de Barcelona (UB).2Research Group MODES, Department of Mathematics, CITIC, Universidade da Coruna ˜and ITMATI.Received: April 2023Accepted: January 2024 -2Conditional likelihood based inference on single-index models for motor insurance claim severity tail of the severity distribution. This problem could be addressed by quantile regres-sion, for fxed quantile levels, but this could potentially lead to contradictory results forclose quantiles. Modelling the cost of claims conditional on covariate information hasremained a bottleneck for insurance companies, as a result of which average costs areused in practice worldwide. We address this problem also considering data on drivingpatterns and driving conditions, a type of information that is available through sensordata regularly collected by insurtech frms. Some new motor insurance rate makingschemes are based on near-miss telematics information which measures the propensityof risky events that do not always lead to an accident (see Guillen et al., 2019, 2020 andGuillen, Nielsen and P ´ ın, 2021). Risk scores such as the ones obtained with erez-Mar ´index-models can
risky events that do not always lead to an accident (see Guillen et al., 2019, 2020 andGuillen, Nielsen and P ´ ın, 2021). Risk scores such as the ones obtained with erez-Mar ´index-models can be combined with the evaluation of near-miss information to improvethe performance of predictive modelling in motor insurance pricing.Single-index regression models are semiparametric methods for generalising linearregression. They specify the dependence between a random variable Y(here the cost ofa traffc accident, or claim severity) and a d-dimensional vector Xas follows (see H ¨ardleet al., 1993): Y= mθ⊤X+ ε, (1)where θ is a vector of unknown parameters, mis an unknown smooth function, and ε isa random variable with zero-mean conditional on X.Traditional approaches for estimating the linear predictor coeffcients θ and the func-tionmare based on the conditional expectation rather than on the whole conditional dis-tribution and, as a consequence, they are vulnerable to the presence of extremes, heavytails or strong asymmetry, as in many applications. Our contribution is to extend themaximum likelihood estimation of (1) and, in so doing, to open the door to single-indexconditional distribution modelling which has enormous potential for a range of applica-tions.In order to estimate the vector θ, H¨ardle, Hall and Ichimura (1993) proposed thedirect minimisation of the residual sum of squares, so their estimator isnh i2θˆ= argminθ ∑ Yi− mˆiθ⊤Xi, i=1where (X1,Y1),..., (Xn,Yn) are iid observations of the covariates and the dependent vari-able and mˆiindicates the leave-one-out kernel estimator of m. Alternatively, Hristache,Juditsky and Spokoiny (2001) analysed the average derivative estimator of the vectorof parameters in the index model, introduced by Stoker (1986) and as subsequentlyemployed by Powell, Stock and Stoker (1989). Hristache et al. (2001) presented themethod for estimating the vector of coeffcients, θ , by minimising an M−function, witha score function ψ, that again compares Yiwith a nonparametric estimator mˆ(·), i.e., � argminθ ∑ni=1ψ Yi,mˆθ ⊤Xi. All these methods ignore the shape of the conditionaldistribution because they are based on ftting the conditional expectation.Delecroix, H ¨ardle and Hristache (2003) investigated the pseudo-maximum likeli-hood estimation of θ in (1). They proposed starting from a preliminary√ n-consistent 3 Catalina Bolanc ´e, Ricardo Cao and Montserrat Guillen estimator and, subsequently, correcting it with the gradient and the Hessian of the log-likelihood function. They showed that the corrected estimator is effcient. Previously,Klein and Spady (1993) had analysed the maximum likelihood estimation of θ but onlyfor a binary response dependent variable. In the context of survival data with censoredobservations, Strzalkowska-Kominiak and Cao (2013) investigated maximum likelihoodalternatives based on the kernel estimation of the conditional distribution and showedthat previous methods for censored data could be
and Cao (2013) investigated maximum likelihoodalternatives based on the kernel estimation of the conditional distribution and showedthat previous methods for censored data could be improved.Nonparametric regression is more general than the single-index model specifed in(1). Indeed, it emanates from a more general specifcation Y= m(X) + ε, where theaim is to estimate the regression curve m(x) = E(Y\|X= x); H¨ardle (1990). However,in practice, nonparametric regression presents two considerable challenges. First, es-timation becomes increasingly diffcult as the number of covariates rises (the curse ofdimensionality). The second challenge is that any interpretation of the effects of the ex-planatory variables cannot be carried out directly and it is necessary to plot the differentrelations to explore these effects. Another alternative to the single-index model is thegeneralised additive model (see Hastie and Tibshirani, 1990); however, it faces the samechallenges as those described for nonparametric regression.Here, a new maximum likelihood estimator of θ in (1) is proposed, inspired by thework of Strzalkowska-Kominiak and Cao (2013) with right-censored data. As theseauthors proposed we use two different smoothing parameters: one associated with thedistribution of Yand the other one associated with the distribution of the index θ⊤X.The new theoretical results that we present in Section 2for uncensored data do notfollow directly as a particular case of Strzalkowska-Kominiak and Cao (2013), sincesome assumptions of the censored data case can be relaxed or dropped. In this paper,we deduce the covariance matrix that can be easily estimated using a kernel estimator.We evaluate the inference power of the statistical test for the covariate effects deducedfrom our maximum likelihood estimator. Details on the method, some results of thesimulation study and proofs are available in the Supplementary Material.We show the superiority of our estimator, in particular, when there are extreme val-ues, like in our application where we observe only a few severe accidents. Additionally,we show that the results of the estimated index model are easily interpretable from dif-ferent points of view, for example, for the prediction of conditional mean, quantiles andmarginal effects.We analyse a data set obtained from a specifc portfolio from an insurance companyin Spain. The portfolio is made up of a small group of policyholders under 35 years ofage, who have underwritten a new insurance contract that requires a telematics device tobe installed in their vehicle. The data set contains information on mean yearly claim costper policy and on telematic and non-telematic characteristics. Our aim is to fnd the in-fuence of telematic information on pricing compared to a traditional approach with onlyclassical non-telematic variables. The data set is available at SORT-BCG/. We observe how the mean yearly claim cost per policy does not changewith a linear index; however, the shape of
with onlyclassical non-telematic variables. The data set is available at SORT-BCG/. We observe how the mean yearly claim cost per policy does not changewith a linear index; however, the shape of the distribution depends on a linear index,something that could be considered when calculating the premium. 4Conditional likelihood based inference on single-index models for motor insurance claim severity In asimulation study presented in Section 3, the fnite-sample properties of our pro-posal are compared with several alternative methods for different distributions with het-erogeneity in the location and in the scale parameters. We also carry out basic inferenceabout the estimators. In addition, we evaluate how the results are affected when the co-variates are correlated and binary explanatory variables are included. Note that Hall andYao(2005) and Newey and Stoker (1993) only consider continuous covariates; indeed,not many papers to date have dealt with discrete covariates in single-index models. Oneexception is Horowitz and H ¨ardle (1996), who focused on analysing a direct estimatorfor the effect of the discrete covariates. Elsewhere, methods such as those proposed byH¨ardle et al. (1993), Hristache et al. (2001) and Delecroix et al. (2003), while allowingdummy (binary) variables to be incorporated, do not consider the consequences of theirinclusion.2. Methods Let us denote the vector of covariates X= (X1,..., Xd)⊤ and let f(·\|x) be the densityfunction of Ygiven X= x, where x = (x1,..., xd) is a fxed vector where f(y\|x) = fθ0(y\|θ0⊤x), where fθ0(·\|θ0⊤x) is the conditional density of Ygiven θ0⊤X= θ0⊤x andθ0isthe parameter vector to be estimated. Furthermore, we assume that F(y\|x) = Fθ0(y\|θ0⊤x) is its conditional cumulative distribution function. For any θ0and any nonzero real num-berλ , then vector θ0can be replaced by λθ0. This means that the conditional distributionof the response given X= x only depends on this covariate vector via the linear combina-tiont= θ0⊤x. If we choose any nonzero real number λ , then, since there is a one-to-onecorrespondence between tandλt, it is also true that the conditional distribution only de-pends on the covariate vector via the linear combination λθ0⊤x. Consequently, infnitelymultiple choices exist for the single-index parameter vector θ0. The usual way to solvethis identifcation problem is to introduce a scale constraint, for example \|\|θ0\|\| = 1 orfxing one component of θ0to be equal to one. In practice, the identifcation problemimplies that the signs of the effects of the covariates on the dependent variable are notidentifed but are comparable, i.e., two parameters with different sign indicate oppositeeffects and, if variables are measured in the same scale, then their corresponding param-eter estimates can be compared directly.Let(X1,Y1),...,(Xn,Yn) be a random sample of the dependent variable and the co-variates, where Xi= (Xi1,..., Xid)⊤ and it is assumed that at least one covariate is con-tinuous. Let Kbe a
directly.Let(X1,Y1),...,(Xn,Yn) be a random sample of the dependent variable and the co-variates, where Xi= (Xi1,..., Xid)⊤ and it is assumed that at least one covariate is con-tinuous. Let Kbe a nonnegative kernel and h1,h2two positive bandwidths. In line withBashtannyk and Hyndman (2001), the kernel conditional density estimator is:rˆ(t,y)fˆθ (y\|t) = sˆ(t) , (2)where n1 t− θ ⊤Xisˆ(t) = s(t) = ∑ K ˆh1nh1i=1h1(3) 5 Catalina Bolanc ´e, Ricardo Cao and Montserrat Guillen and the product bivariate kernel density estimator is used for rˆ(t,y); see Chapter 6 ofScott (2015). The product kernel is just a simple way to smooth using multiplicativeweights, so: n1 t− θ⊤Xi y−Yirˆ(t,y) = rˆh1,h2(t,y) = ∑ K K . (4)nh1h2i=1h1 h2We use a Gaussian kernel, and the smoothing parameters are calculated using alter -native criteria considering the estimator type, i.e., the parameter vector, the conditionaldensity, the conditional distribution or the conditional mean.In line with Hall, Wolff and Yao (1999), the kernel estimator of the conditionaldistribution function is:Fbθ (y\|t) = Rb(t,y) , sˆ(t) where n1 t− θ⊤Xi y−YiRb(t,y) = Rbh1,h2(t,y) = ∑ K Knh1i=1h1 h2andK is the kernel distribution function.2.1. Maximum conditional likelihood estimation If we know Fθ except for the value of the index vector θ (a highly unrealistic assump-tion), then we can defne the following theoretical conditional likelihood function:nLn(θ) = ∏ fθ (Yi\|θ⊤Xi). ˜i=1Maximising this function is equivalent to maximising its logarithm:n1� 1ℓ˜n(θ) = logL˜n(θ ) = ∑ logfθ (Yi\|θ ⊤Xi). (5)n ni=1Here, the ideal estimator should maximise the theoretical log-likelihoodθ˜n= argmax ℓ˜n(θ). θ In practice, fθ (orFθ ) is unknown and so, we need to estimate it and plug it into thelogarithm of the theoretical conditional likelihood function.We propose to maximise the kernel estimation of the log-likelihood function de-fned in (5) with respect toθ and to the two smoothing parameters, h1andh2. At thispoint, we note that, in the kernel estimation, when a smoothing parameter selector is ob-tained by optimising some criteria, such as the integrated square error or the likelihoodfunction, which required computing a kernel estimator; using the whole observed data -6Conditional likelihood based inference on single-index models for motor insurance claim severity set,(X1,Y1),...,(Xn,Yn), produces undersmoothing of the optimal smoothing parametervalues; see Silverman (1986). As a consequence, we need to modify the estimated like-lihood with a leaving-one-out procedure so as not to pick artifcially small bandwidths.Letfˆ−i(Yi\|θ⊤Xi) be the estimator defned in (2), where the sum in (3) and (4) runs overθ j̸= i. Then, we defne the leaving-one-out estimated conditional log-likelihood:n1ℓˆn(θ) = ∑ logfˆ−i(Yi\|θ⊤Xi). (6)θni=1Given h1andh2, the fnal maximum conditional likelihood estimator is defned asθˆn= argmax ℓˆn(θ). θ The estimation procedure including the two smoothing parameters h1andh2will bedescribed in sub-section 2.3. A
the fnal maximum conditional likelihood estimator is defned asθˆn= argmax ℓˆn(θ). θ The estimation procedure including the two smoothing parameters h1andh2will bedescribed in sub-section 2.3. A similar procedure based on the leave-one-out estimatorof the hazard rate model was proposed by van den Berg et al. (2021). We point outthat it can be diffcult to avoid local optima in the maximisation of the log-likelihood in(6). Considering the existence of local optima, in the described estimation procedure wechecked how initial values for the smoothing parameters affect the fnal estimation. Wehave observed that the fnal estimation is practically not affected by the initial values ofthe covariate coeffcients.2.2. Properties In this sub-section we study the properties of θˆn. Let the score function be defned as theexpected log-likelihood:ℓ(θ ) = E(ℓ˜n(θ )). We start by proving that the true parameter vector, θ0, can be characterised as the max-imiser of the score function. The existence of that function is the only condition required:A1:E(logfθ (Yi\|θ ⊤Xi)) < ∞ for anyθ Theorem 1. The true single-index parameter, θ0, is the maximiser of the score function,i.e.,θ 0= argmax θ ℓ(θ).To establish the main results for the estimator, we need to assume some furtherconditions:A2:E(X\|θ0⊤X,Y) = E(X\|θ0⊤X) A3:E(XX⊤) < ∞ componentwise.Condition A2 is a technical one needed to prove our theoretical results. It essentiallymeans that all the information needed to predict the values of the explanatory variables 7 Catalina Bolanc ´e, Ricardo Cao and Montserrat Guillen given the index and the response variable is contained just in the index. Assumption A2also implies exogeneity of the explanatory variables, i.e., covariates are known previousto the response.The two bandwidthsh1,h2should fulfll the following conditionsA4:√ nh41→ 0,√ nh22→ 0,nh61→ ∞ andh 1,h2→ 0 whenn → ∞.Consider fθ0the bivariate joint density function of (θ0⊤X,Y) andfθ0⊤Xthe marginaldensity function of θ0⊤X. Finally, let ℓ(θ0) = ∇θ ℓ(θ )\|θ denote the gradient of ℓ(θ) =θ0overθ evaluated in θ0. Further, let ℓ(θ) denote the Hessian matrix of ℓ(θ). Thefollowing regularity conditions are also assumed.∂ j∂ kdjdjA5: The derivatives fθ0(u,v),dju⊤X(u) anddjuE(X\|θ0⊤X= u) exist for j= ∂ ju∂ kvfθ01,2,3 andk = 1,2.A6: The function h(x,y) = ∂ θ ∂ jfθ (θ ⊤x,y)θ is continuous and∂∂ 2θ 2jfθ (θ0⊤x,y)θ =θ0 =θ0exists.A7: The Hessian matrix ℓ(θ ∗) is positive defnite for θ ∗ belonging to a neighbourhoodofθ 0.Now we can state the frst result for the proposed estimator.h i−1Lemma 1. Under A1, A4 and A6 we have θˆn− θ0= − ℓˆ(θˆ∗) n n(ℓˆn(θ0) − ℓ(θ0)),where θˆ∗ is between θˆnandθ0.nTheorem 2. Under A1-A7, we haveθ ˆn→ θ0in probability.Theorem 3. Let us assume conditions A1-A7. Then, we have√ n(θˆn− θ0) → N(0,Σ), (7)whereΣ = Σ2Σ1Σ⊤ (8)2, h i−1Σ2= ℓ(θ0) and Σ1= E∇θ log( fθ (Y\|θ ⊤X))θ )(∇θ log( fθ (Y\|θ ⊤X))θ )⊤ =θ0 =θ0Z = (∇θ log( fθ (y\|θ⊤x))θ )(∇θ log( fθ (y\|θ⊤x))θ )⊤ f(x,y)dxdy. =θ0 =θ0All the proofs can be found in the Supplementary
h i−1Σ2= ℓ(θ0) and Σ1= E∇θ log( fθ (Y\|θ ⊤X))θ )(∇θ log( fθ (Y\|θ ⊤X))θ )⊤ =θ0 =θ0Z = (∇θ log( fθ (y\|θ⊤x))θ )(∇θ log( fθ (y\|θ⊤x))θ )⊤ f(x,y)dxdy. =θ0 =θ0All the proofs can be found in the Supplementary Material.The asymptotic variance-covariance matrix in (8) is different from the one obtainedby Delecroix et al. (2003). These authors obtained this matrix from ℓ˜n(θ ) defned in (5) 8Conditional likelihood based inference on single-index models for motor insurance claim severity and took into account the almost sure convergence of the parameter estimator and theweak convergence of ℓˆn(θ ),defned in (6), and some of its partial derivatives. Instead,to obtain the asymptotic variance-covariance matrix, we take into account that θ0is es-timated by maximising the kernel estimator of the conditional likelihood function ℓˆn(θ) defned in (6).2.3. Estimation procedure To obtain θˆn,h1andh2we have used an algorithm in two steps. The frst step aims to ob-tainθˆnby maximising the likelihood function in (6) given fxed values for the smoothingparameters h1andh2. In the second step the smoothing parameters are recalculated bymaximising the same likelihood function given the values of θˆnobtained in the previousstep. Both steps are repeated until convergence. In the frst step the initial values of thesmoothing parameters are given by h1= aσˆθ⊤Xn−213, where a> 0andσˆθ ⊤XandσˆYarethe empirical standard deviations (see Silverman (1986) for rule-of-thumb smoothing parameters in kernel density estimation). The sample size orders,n−213, respectively for the two bandwidths, are chosen in order to fulfll theasymptotic assumptions for the bandwidths needed for Condition A4. We have observedthat initial values of the smoothing parameters considerably affect the fnal estimation.Initially we used a= 1 but it is recommended to consider a grid of values around 1.The initial values of the covariate coeffcients hardly affect the results, so to start thealgorithm we set all these coeffcients equal to 1. To maximise the likelihood func-tion in the frst step, we use the function “optim()” with the default optimization method(“Nelder-Mead”) of the “stats” Rpackage. In the second step, to recalculate the values h1andh2we also use function “optim()” but with optimization method ”L-BFGS-B”. Weneed to defne limits for the smoothing parameters because it is known that ℓˆn(θ) → ∞ (1)σθ⊤Xn−213) forh1and1 2(2)σYn−413) forh 2, for some c1< c, j= 1,2.1 2 2Our two-step algorithm is designed to guarantee the conditions established in thetheoretical properties shown in the previous sub-section. In practice, we are selecting thebest estimation in a set of pre-fxed smoothing parameters which are calculated takinginto account the sample size and the scale of the dependent variable and the index.To estimate the variance-covariance matrix in (8)we calculate the correspondingderivatives of the leave-one-out kernel estimation of conditional log-likelihood defnedin(6). Asymptotic normality inference,
the variance-covariance matrix in (8)we calculate the correspondingderivatives of the leave-one-out kernel estimation of conditional log-likelihood defnedin(6). Asymptotic normality inference, based on (7),is carried out using the esti-mated variance-covariance matrix, replacing theoretical derivatives by estimated ones(kernel estimator of the gradient ∇θ log( fθ (y\|θ ⊤x))θ is direct). For kernel estimator=θ0ofℓ(θ0) see Lemma 9 in the Supplementary Material.2.4. Marginal effects estimation For a given θ = θ0, using the conditional distribution function we can obtain the p-th conditional quantile: Qθ (p\|θ ⊤x) = F−1(p\|θ ⊤x), i.e., Fθ (yp\|θ⊤x) = pwhere p∈θ 9 Catalina Bolanc ´e, Ricardo Cao and Montserrat Guillen (0,1). As in any generalised linear model, comparing marginal effects is equivalent tocomparing parameters, i.e., for two covariatesX kandXk′ , with k̸= k′, we obtain:∂ Qθ (p\|θ ⊤x) ∂ xk= θk,∂ Qθ (p\|θ ⊤x) θk′ ∂ xk′ where:∂ Fθ (Qθ (p\|θ ⊤x)\|t) ·∂ Qθ (p\|θ ⊤x) ∂tθkt=θ⊤x = − . (9)∂ xk fθ (Qθ (p\|θ ⊤x)\|θ⊤x) For estimating the marginal effects we will use kernel estimators for fθ (y\|θ ⊤x),Fθ (y\|θ ⊤x) and their derivatives, as shown below.The kernel estimator of the index marginal effects on the conditional distributionfunction is:" # ∂ Fbθ (y\|t= θ⊤x) Rˆ′ (θ⊤x,y) sˆ′ (θ⊤x)h1,h2 h1= − Fbθ (y\|θ ⊤x) ,∂t ˆ(θ ⊤x) ˆ(θ⊤x) sh1 sh1where n1 t− θ⊤Xi y−YiRˆ′ (t,y) = ∑ K′ Kh1,h2nh21h2 h2 i=1h1and n1 t− θ⊤Xi ′ sˆh1(t) = ∑ K′ ,nh2h1 1i=1where K′ is the frst derivative of the kernel.In this paper, we obtained the marginal effects using kernels estimators of the differ -ent functions that appear in the expression (9). The smoothing parameters of the kernelestimator of conditional density can be calculated using the sample size orders of ref-erence rules obtained in Bashtannyk and Hyndman (2001). The kernel estimator of theconditional distribution and its derivatives are obtained directly from the estimated con-ditional density. Considering that in this paper the aim of estimating marginal effectsis purely descriptive, we have obtained the values of smoothing parameters subjectivelyfrom graphic visualization. However, a double-cross-validation approach as suggestedvan den Berg et al. (2021) can be used.2.5. Scoring rules for prediction To evaluate the goodness of ft and the predictive capacity of the single-index model, avariety of measures is available. Gneiting and Raftery (2007) present an exhaustive re-view of different families of scoring rules for moments, density and distributional fore-casts. We use three types of score described in Gneiting and Raftery (2007). 10Conditional likelihood based inference on single-index models for motor insurance claim severity The predictive model choice criterion (PMCC) selects the best model based on thefrst two moments of the predicted values, i.e., the mean and the variance, as followsnh i2 ˆ2PMCC = − 1∑ Yi− mˆθ ⊤Xi− σ θ ⊤Xi, (10)ni=1� � where mˆθ ⊤Xiis the kernel estimator of the conditional expectation E Y i\|θ ⊤Xiand� ˆ2σ
values, i.e., the mean and the variance, as followsnh i2 ˆ2PMCC = − 1∑ Yi− mˆθ ⊤Xi− σ θ ⊤Xi, (10)ni=1� � where mˆθ ⊤Xiis the kernel estimator of the conditional expectation E Y i\|θ ⊤Xiand� ˆ2σ θ⊤Xiis estimated with the kernel estimates of both expectations as follows: h i2σˆ2θ ⊤Xi= EˆYi2\|θ⊤Xi− EˆYi\|θ⊤Xi, where ∑n t−θ ⊤Xi i=1Kh1YiEˆYi\|θ⊤Xi= mˆθ⊤Xi= ∑n t−θ ⊤Xii=1Kh1and t−θ ⊤XiY2 ∑ni=1Kh1 iEˆ = . Yi2\|θ⊤Xi∑n t−θ ⊤Xii=1Kh1Here h1is calculated using the optimal sample size order (n−1/5) to estimate the condi-tional expectation and considering the scale of the dependent variables.The logarithmic scoring rule is calculated asnh i ℓˆ(θ) = ∑ log fˆYi\|θ ⊤Xi. (11)i=1From lˆ(θ ) other widely used criteria such as the AIC (Akaike Information Criterion) andthe BIC (Bayesian Information Criterion) can be obtained.For the p-quantile prediction of the dependent variable, Y, the goodness of ft crite-rion proposed by Koenker and Bassett (1978) for quantile regression is:n1QE p(θ) = ∑ p Y i− Qˆθ (p\|θ ⊤Xi)ni=1,Yi>Qˆθ (p\|θ ⊤Xi) n+ 1∑ (1− p) Yi− Qˆθ (p\|θ⊤Xi) , (12)ni=1,Yi≤Qˆθ (p\|θ ⊤Xi) where Qˆθ (p\|θ ⊤Xi) is the kernel conditional quantile estimator based on the kernel es-timator of the conditional distribution function. For a set of probabilities p1,..., pk, we1 1defne QE= k∑kj=1QE pj(θ ) and its corresponding weighted version, WQE = j=1 k∑kpjQE pj(θ ). 11 Catalina Bolanc ´e, Ricardo Cao and Montserrat Guillen 3. Simulation study We carry out a simulation study, the aim being to evaluate the fnite-sample propertiesof our estimator. The properties of the parameter estimator, θˆ, are summarised in theSupplementary Material and the basic inferences about the value of these parameters arepresented in this section. The results are obtained using a Gaussian kernel.We compare the variance, the bias and the mean square error (MSE) of the estimatedparameters in the vector θˆ, using our fexible maximum conditional likelihood (FMCL)estimator and three alternatives. The frst is based on ftting the single-index model toindividual conditional expected values as proposed by H ¨ardle et al. (1993) (hereinafter,HHI). The second alternative is based on Delecroix et al. (2003) (hereinafter, DHH),where we use as our initial parameters those obtained with the HHI method which are√ n-consistent. The third is the direct method proposed by Hristache et al. (2001) (here-inafter, HJS).We analyse six different conditional distributions for the dependent variable Y, twosymmetric distributions (zero skewness) and four right-skewed distributions. The con-ditional distributions are shown in Table 1.Table 1. Conditional distributions for dependent variable as a function of the linear index θ⊤x for the simulation study.Skewness Distribution Parameters DensityZeronormallogistic(µ = θ ⊤x,σ = \|θ ⊤x\|) (µ = θ ⊤x,σ = \|θ ⊤x\|) x)21 (y− θ⊤p exp− 2π\|θ ⊤x\|2 2\|θ ⊤x\|2 (y− θ ⊤x)exp1 \|θ ⊤x\| \|θ ⊤x\| (y− θ⊤x)1+ exp\|θ⊤x\| PositivelognormalWeibullChampernowne(µ = θ ⊤x,σ = \|θ ⊤x\|) (α = 1, σ = \|θ ⊤x\|) (α = 1,M= \|θ ⊤x\|) (α
⊤x,σ = \|θ ⊤x\|) x)21 (y− θ⊤p exp− 2π\|θ ⊤x\|2 2\|θ ⊤x\|2 (y− θ ⊤x)exp1 \|θ ⊤x\| \|θ ⊤x\| (y− θ⊤x)1+ exp\|θ⊤x\| PositivelognormalWeibullChampernowne(µ = θ ⊤x,σ = \|θ ⊤x\|) (α = 1, σ = \|θ ⊤x\|) (α = 1,M= \|θ ⊤x\|) (α = 2,M= \|θ ⊤x\|) 1 (ln(y) − θ⊤x)2p exp− 2π\|θ ⊤x\|2 2\|θ⊤x\|2y 1 yexp− \|θ ⊤x\| \|θ ⊤x\| \|θ ⊤x\| 2(y+ \|θ ⊤x\|) 2\|θ ⊤x\|2y2(y2+ \|θ ⊤x\|2) 12Conditional likelihood based inference on single-index models for motor insurance claim severity For our two choices of symmetric distribution, the logistic distribution has morekurtosis and heavier tails than the normal distribution. If we compare our selection ofright-skewed distributions, we fnd that the Champernowne or log-logistic has a heaviertail than the lognormal and the Weibull; see Buch-Larsen et al. (2005) for a descriptionof the Champernowne distribution.In our simulation study, we use six vectors of covariates Xthat we identify as vec-tors V1, V2, V3, V4, V5 and V6. For the frst three θ⊤ = (1,1.3,0.5) and for the fourthθ ⊤ = (1,1.3,0.5,0.8). The values in vector V1 are generated from three uncorrelatedstandard normal distributions. The vectors V2 and V3 are trivariate normal distributionswith correlated marginals. For V2 the components are three standard normal distribu-tions whose covariances are cov(Xk,Xk′ ) = 0.3 for k≠ k′ andk,k′ = 1,2,3. The sameholds for V3 but with covariances cov(X1,X2) = cov(X2,X3) = 0.7 and cov(X1,X3) = 0.5.Vector V4 consists of V1 and a binary variable whose values are generated from aBernoulli distribution with probability 0. 4, independent of the three components of V1.Furthermore, the number of categorical covariates is usually greater than one. We havecarried out an alternative simulation study using two new vectors of covariates V5 andV6, with θ⊤ = (1,1.3,0.5,0.8). Vector V5 consists of two independent standard normalvariables and two binary variables whose values are generated from two Bernoulli dis-tributions with probabilities 0. 4 and 0. 7, respectively. The covariate vector V6 includesthe same two binary variables, one lognormal with mean 0 and σ equal to 0. 5 and onewith a standard normal distribution.We generate 500 samples of size n= 100, 500 and 2, 000 and calculate the bias, thestandard deviation (STD) and the MSE of the estimators using each method, FMCL,HHI, DHH and HJS. The results of the simulation study show that the proposed FMCLestimator is the most suitable when the conditional distribution is right-skewed and alsowhen the tail of the conditional distribution is heavy. Moreover, the FMCL is morerobust to multicollinearity and to the presence of binary and asymmetric covariates.3.1. Basic inference Power analysis of hypothesis tests is fundamental to determining whether the effect of acovariate is signifcantly different from zero. The null hypothesis for each parameter isH0:θk= 0, k= 1,..., dand as an alternative hypothesis we assume that the sign of theparameter is known, i.e., H1:θk> 0, k= 1,..., d. The statistic test is Z= θˆjse(θˆ2− θˆ3). 13 Catalina Bolanc
isH0:θk= 0, k= 1,..., dand as an alternative hypothesis we assume that the sign of theparameter is known, i.e., H1:θk> 0, k= 1,..., d. The statistic test is Z= θˆjse(θˆ2− θˆ3). 13 Catalina Bolanc ´e, Ricardo Cao and Montserrat Guillen Table 2. Power of the test for skewed distributions. The values are calculated using the 500samples for each skewed distribution in Table 1.H0Lognormaln= 500 n= 2,000Weibulln= 500 n= 2,000Champernowneα = 1n= 500 n= 2, 000Champernowne α = 2n= 500 n= 2, 000V1V4V1V4θ2= 0θ3= 0θ2= 0θ3= 0θ4= 0θ2= θ3θ2= θ31.000 1.0001.000 1.0001.000 1.0001.000 1.0001.000 1.0001.000 1.0001.000 1.0000.864 0.9960.876 0.9980.856 1.0000.828 1.0000.770 0.9840.882 0.9960.662 1.0000.722 0.9700.702 0.9720.636 0.9080.622 0.9020.584 0.8620.730 0.9760.598 0.8800.984 0.9980.992 1.0001.000 1.0001.000 1.0000.996 1.0000.988 1.0000.998 1.000Table 3. Percent of no-rejection of null hypothesis. The values are calculated using the 200samples for each distribution in Table 1.H0Normaln= 500 n= 2000Logisticn= 500 n= 2000Lognormaln= 500 n= 2000V1V4θ4= 0θ5= 00.848 0.9550.828 0.9800.942 0.9850.992 0.9800.696 0.8500.345 0.890H0Weibulln= 500 n= 2000Champernowneα = 1n= 500 n= 2000Champernowne α = 2n= 500 n= 2000V1V4θ4= 0θ5= 00.850 0.9650.924 0.9650.530 0.5700.478 0.7950.752 0.7200.720 0.770The results for symmetric distributions have a power about 100% for almost all testswhen n≥ 500, these results are shown in the Supplementary Material. Here we focus onthe results for the power of tests for skewed distributions.Table 2 shows the powers of the two tests proposed for skewed distributions. Bothtests are at the 95% confdence level. These results indicate that when n= 500 the powerdecreases considerably for the Weibull and the Champernowne distribution with α = 1,compared to a larger sample size, n= 2,000.To analyse the percent of times the null hypothesis that the parameter is equal tozero is not rejected, we have designed an alternative reduced simulation study that con-sists of adding a new covariate with associated parameter equal zero in the estimationprocedure; this implies to re-estimate the parameters. To reduce the computation time,instead of 500 replicates, we use 200 replicates of sizes n= 500 and n= 2,000. Thenull hypothesis is H0:θj= 0, j= 4,5, and the results of the percent of no-rejectionof the null hypothesis, for the models described in Table 1 and using extended covariatevectors, are shown in Table 3. For n= 500 the results for skewed distributions are poorerthan those obtained for a symmetric distributions. For n= 2,000, in general, the resultsimprove compared to a smaller sample size, except for the Champernowne distribution,which is heavy tailed. These results suggest that if the dependent variable is asymmetric,a transformation to achieve a symmetric distribution should be suitable. 14Conditional likelihood based inference on single-index models for motor insurance claim severity 4. Data analysis and model estimations of automobile claim costs In
distribution should be suitable. 14Conditional likelihood based inference on single-index models for motor insurance claim severity 4. Data analysis and model estimations of automobile claim costs In this section we analyse the effect of risk factors on the distribution of the cost perautomobile claim in a real case study. We show that single-index models constitute anew tool for identifying the infuence of some of those covariates that are known to theinsurer at the beginning of the contract or during the coverage period. We estimate thesingle-index model coeffcients with the FMLC method. The results are obtained usinga Gaussian kernel. Some parametric models based on Weibull, gamma, log-normal andlog-logistic distributions, which are not reported here, produced poor fts. Furthermore,signifcant effects of the covariates were not found.We analyse a data set obtained from a Spanish insurance company. The originalportfol
www.vtpi.org Info@vtpi.org 250-508-5150 © 2001 -2023 Todd Alexander Litman All Rights Reserved Distance -Based Vehicle Insurance Feasibility, Costs and Benefits Comprehensive Technical Report 10 March 2023 By Todd Litman Victoria Transport Policy Institute Abstract Vehicle insurance is a significant portion of total vehicle costs. A typical motorist spends nearly as much on insurance as on fuel. Insurance is generally considered a fixed cost with respect to vehicle use. A motorist who reduces mileage does not usually receive comparable insurance cost savings. Distance -based insurance converts insurance to a variable cost with respect to vehicle travel, so premiums are directly affected by annual mileage. The more you drive the more you pay, and the less you drive the more you save. Distance -based pricing makes vehicle insurance more actuarially accurate (premiums better reflect the claim costs of each vehicle), and can help reduce total insurance costs, vehicle crashes, traffic congestion, facility costs, energy consumption and environmental impacts. This report investi gates the feasibility, benefits and costs of implementing distance -based motor vehicle insurance. It compares several distance -based insurance pricing options, and evaluates related concerns and criticisms. The analysis indicates that distance -based pricin g is technically and economically feasible, and can provide significant benefits to motorists and society. Distance -Based Vehicle Insurance; Technical Report Victoria Transport Policy Institute 1 Table of Contents Executive Summary ................................ ................................ ................................ ......................... 2 Introduction ................................ ................................ ................................ ................................ ..... 6 Automobile Pricing Practices ................................ ................................ ................................ ........... 8 Current Vehicle Insurance Pricing ................................ ................................ ................................ .............. 8 Factors Influencing Insurance Prices ................................ ................................ ................................ ....... 10 How Pricing Affects Vehicle Trave l ................................ ................................ ................................ .......... 12 Relationship Between Mileage and Crash Costs ................................ ................................ ........... 13 Crash and Claim Rates ................................ ................................ ................................ ............................. 13 Pricing Options ................................ ................................ ................................ .............................. 34 1. Mileage Rate Factor (KRF) ................................ ................................
................................ ................................ .............................. 34 1. Mileage Rate Factor (KRF) ................................ ................................ ................................ .............. 34 2. Pay-at-the-Pump (PATP) ................................ ................................ ................................ ................ 39 3. Usage -Based Premiums ................................ ................................ ................................ .................. 47 4. GPS-Based Pricing ................................ ................................ ................................ .......................... 62 Summary of Distance -Based Pricing Options ................................ ................................ .......................... 67 Comparing Distance -Based Insurance Options ................................ ................................ ............. 68 1. Actuarial Accuracy ................................ ................................ ................................ .......................... 68 2. Implementation Costs ................................ ................................ ................................ .................... 69 3. Equity ................................ ................................ ................................ ................................ ............. 70 4. Consumer Impacts ................................ ................................ ................................ ......................... 71 5. Public Acceptability ................................ ................................ ................................ ........................ 74 6. Travel Reduction Impacts ................................ ................................ ................................ ............... 75 7. Road Safety ................................ ................................ ................................ ................................ .... 77 8. Congestion and Facility Cost Savings ................................ ................................ ............................. 78 9. Energy and Emission ................................ ................................ ................................ ...................... 79 10. Economic Efficiency and Development ................................ ................................ ..................... 80 Summary ................................ ................................ ................................ ................................ ........ 81 Barriers, Costs and Concerns ................................ ................................ ................................ ......... 83 1. Transition and Tra nsaction Costs ................................ ................................ ................................ ... 83 2. Transaction Costs ................................ ................................ ................................
................................ ................................ ... 83 2. Transaction Costs ................................ ................................ ................................ ........................... 83 3. Financial Risks ................................ ................................ ................................ ................................ 83 Conclusions ................................ ................................ ................................ ................................ .... 86 References and Resources ................................ ................................ ................................ ............ 90 Appendices (Separate Document Available at the VTPI website) 1. Evaluation Criteria 2. Vehicle Operating Cost Estimates 3. Estimate of Cross -Border and Illegally Untaxed Fuel Use 4. Odometer Auditing 5. Criticism of Distance -Based Insurance 6. Press Coverage of Distance -Based Insurance Distance -Based Vehicle Insurance; Technical Report Victoria Transport Policy Institute 2 Executive Summary This study investigates the feasibility, benefits and costs of implementing dista nce-based motor vehicle insurance. It is based on a literature review, analysis of insurance claim data, comparisons of different distance -based pricing options, and evaluation of concerns that have been raised about distance -based pricing. Vehicle insura nce is a significant portion of total vehicle costs. A typical motorist spends almost as much on insurance as on fuel. Insurance is generally considered a fixed cost with respect to vehicle use. A reduction in mileage does not usually provide a comparable reduction in insurance premiums. Research described in this report indicates that within existing price categories, annual claims increase with annual vehicle mileage, as illustrated below. Mileage is just one of several factors that affect crash rates. It would not be actuarially accurate to use mileage instead of other rating factors, for example, to charge all motorists the same per -mile insurance fee, but actuarial accuracy improves significantly if annual mileage is incorporated in addition to existi ng rate factors. Any other price structure overcharges low-mileage motorists and undercharges high -mileage motorists. Crash Rates by Annual Vehicle Mileage 0.000.020.040.060.080.10<55- <1010- <15 15- <20 20- <25 25- <30Annual Vehicle Kilometres (1,000s)Crash-Related Claims Per YearTotalNon-CulpableCulpableCasualty Crashes per vehicle tend to increase with annual mileage. Distanc e-based insurance reflects the principle that prices should be based on costs. It gives consumers a new way to save money by returning to individual motorists the insurance cost savings that result when they drive less. Motorists who continue their current mileage would be no worse off on average then they are now (excepting any additional transaction costs), while those who reduce their mileage save money. Distance -based pricing can
their current mileage would be no worse off on average then they are now (excepting any additional transaction costs), while those who reduce their mileage save money. Distance -based pricing can help achieve several public policy goals including actuarial accuracy, e quity, affordability, road safety, consumer savings and choice. It helps reduce traffic congestion, road and parking facility cost savings, and environmental impacts. It can reduce the need for cross -subsidies currently required to provide “affordable” unlimited -mileage coverage to high -risk drivers. Distance -Based Vehicle Insurance; Technical Report Victoria Transport Policy Institute 3 This study evaluated several distance -based pricing options: 1. Mileage Rate Factor (MRF) incorporates an annual mileage rate factor into the existing rate system. It is the easiest option to implement, but is constrained by the weight that can be placed on self -reported mileage estimates. Its travel impacts and benefits are small. 2. Pay-at-the-Pump (PATP) funds basic insurance coverage through a surcharge on fuel sales. It is not actuarially accurate because paym ents are based on vehicle fuel consumption, not risk factors. Less than half of insurance payments would be distance -based, and cross -border and illegal fuel purchases could be major problems. It causes a relatively large reduction in fuel consumption but modest reductions in vehicle travel, providing modest overall benefits. There would probably be little administrative cost savings because motorists would still need to pay registration fees and purchase optional coverage as they do now. 3. Per-Mile Premiums changes the unit of exposure from the vehicle -year to the vehicle -mile, incorporating all existing rating factors. It requires odometer audits to provide accurate mileage data, predicted to cost an average of $6 per vehicle year. It could be mandatory or a consumer option. It significantly improves actuarial accuracy and provides significant consumer savings, particularly to lower income households. Because it causes large reductions in vehicle travel it provides large benefits. As a consumer option it is p redicted to attract 25 -50% of motorists within a few years, and this should increase over time. 4. Per-Minute Premiums uses a small electronic meter to record when an engine operates, predicted to cost $30 per year. This allows rates to vary by time of day. B ecause it can give motorists an extra incentive to reduce their peak -period travel it can provide even greater benefits than Per -Mile Premiums, but the additional equipment costs reduce the net benefits. As a consumer option it is predicted to attract 12 -25% of motorists within a few years. 5. GPS -Based Pricing uses GPS (Global Positioning System) technology to track vehicle travel, allowing insurance prices to reflect when and where a vehicle is driven in addition to existing rating factors. It is predicted t o cost $150 or more per vehicle -year and raises
vehicle travel, allowing insurance prices to reflect when and where a vehicle is driven in addition to existing rating factors. It is predicted t o cost $150 or more per vehicle -year and raises privacy concerns. Installation costs may decline somewhat in the future as more vehicles have factory -equipped GPS transponders. It is most actuarial accurate and can cause the greatest crash reduction per pa rticipating vehicle. However, its high equipment costs offset the direct benefits for most consumers. As a consumer option it is predicted to attract 10% or less of total motorists, so total benefits would be modest for the foreseeable future. The table b elow compares the travel impacts of these options. Travel Impacts of Distance -Based Pricing Options MRF PATP Per-Mile Mandatory Per-Mile Optional Per-Min. Mandatory Per-Min. Optional GPS-Based Portion of market affected 100% 90% 100% 50% 100% 25% 10% Price increase per mile 0.7¢ 1.4¢ 5.6¢ 5.6¢ 5.6¢ 5.6¢ 5.6¢ Reduction per participating veh. 1.0% 5.0% 10% 13% 10% 14% 15% Total vehicle travel reduction 1.0% 4.5% 10% 3.7% 10% 1.8% 0.8% Distance -based insurance can provide significant safety benefi ts. Because most crashes involve multiple vehicles, a reduction in total vehicle mileage produces a proportionally larger reduction in total crash costs, all else being equal. Each 1.0% reduction in vehicle mileage caused by distance -based insurance can re duce total crash costs by 1.4% to 2.0%. Distance -based pricing could reduce total crashes by 15% or more. Distance -Based Vehicle Insurance; Technical Report Victoria Transport Policy Institute 4 Distance -based pricing can help achieve equity objectives. Since annual vehicle mileage tends to increase with income, fixed -price insurance causes l ower -income motorists to subsidize the insurance costs of higher -income motorists within their rate class. Distance -based insurance pricing provides overall savings to lower -income motorists, and would allow some low -income households to own a vehicle for basic mobility that they cannot currently afford. Distance -based pricing lets motorists save money by reducing mileage, an option that is currently unavailable. To illustrate this, consider the situation of somebody who becomes unemployed and so reduces d riving by half. With current pricing, they continue paying the same insurance premiums as when they were employed and commuting, although both their income and chances of an insurance claim decline significantly. They may find insurance costs, and therefor e vehicle ownership, an extreme financial burden. With distance -based pricing, low -income drivers can minimize their insurance costs by minimizing their driving, while still affording a car for essential trips and future work. The table below summarizes the implementation costs and effectiveness at achieving various objectives for the seven distance -based pricing options considered in this study. Summary of Distance -Based Pricing Options
the implementation costs and effectiveness at achieving various objectives for the seven distance -based pricing options considered in this study. Summary of Distance -Based Pricing Options Implementation Costs Effectiveness Mileage Rate Factor Low Low Pay-At-The-Pump High Medium Per-Mile Premiums, Mandatory Low High Per-Mile Premiums, Optional Low Medium Per-Minute Premiums, Mandatory Medium High Per-Minute Premiums, Optional Medium Medium GPS-Based Pricing High Low This table summarizes overall c osts and effectiveness at achieving objectives. This analysis indicates that Mandatory Per -Mile Premiums provides the greatest net benefits due to its relatively low cost and effectiveness at achieving objectives. It would provide direct financial saving s to most motorists, and only a small portion (less than one in five) would perceive significantly higher insurance costs. Optional distance -based pricing results in greater direct consumer benefits per participating vehicle, but smaller total benefits due to low market penetration and the low average mileage of motorists who choose it, resulting in relatively small reductions in total vehicle travel. Distance -based insurance is technically and economically feasible. One insurer has successfully implement ed GPS -Based Pricing, the most difficult and expensive distance -based pricing option. Other options should be far easier to implement. Under some circumstances consumers seem to prefer fixed prices, because it is predictable and minimizes transaction cost s. However, this preference appears to be weak. There is no evidence that consumers have a strong preference for fixed -priced insurance. Given the choice, most motorists who expect to save money would probably choose optional distance -based insurance. There is likely to be strong support for optional distance -based insurance pricing since it increases consumer choice and gives motorists a new opportunity to save money. Consumers are accustomed to being able to choose from various rate structures for Distance -Based Vehicle Insurance; Technical Report Victoria Transport Policy Institute 5 many types of goods, such as telephone service, Internet service and air travel. If cross -subsidies are not allowed between the different pricing pools, an increasing portion of motorists would switch to it over time. There appears to be mixed public support f or mandatory distance -based insurance. Citizens generally support price reforms that increase fairness and affordability, or help solve specific problems such as traffic congestion and pollution, but are skeptical of changes that may be confusing or less c onvenient to use, increase costs, or burden particular groups. PATP appears to be the least popular option. Usage -Based Premiums appears to have about equal levels support and opposition, with responses affected by the concept is described. For example, if described as a reward to consumers who use alternative modes, it tends to have a positive
equal levels support and opposition, with responses affected by the concept is described. For example, if described as a reward to consumers who use alternative modes, it tends to have a positive response, but if presented as a surcharge on higher -mileage motorists, it tends to have a more negative response. This study examined various concerns and criticism s raised about distance -based insurance pricing. Many concerns reflect misunderstanding of the concept, and can be addressed with education. Insurers have five legitimate financial concerns about distance -based insurance. 1) It is possible that the mileage f oregone will be lower than average risk. As a result, premium revenue could decline more than claim costs. 2) Optional distance -based pricing could attract motorists with relatively high per -mile claim costs. 3) With optional distance -based pricing, motorists in multi -vehicle households could shift driving from vehicles with distance -based to fixed -rate premiums. 4) Total premiums would probably decline, assuming distance -based pricing is successful at reducing claims. Although revenue reductions would be offset by reduced claim costs, this would tend to reduce gross crash flow and investment income, which could reduce insurance company profits. 5) Some motorists may try to steal insurance by odometer fraud. However, odometers are increasingly tamper -resistant, and m ost types of fraud could be detected during regular checks and crash investigations. Odometer auditing should provide data comparable in accuracy to that used in other common commercial transactions. Offsetting these risks is the fact that a percentage r eduction in mileage usually provides a proportionally greater reduction in claims. A 1% reduction in mileage typically causes a 1.4% to 1.8% reduction in claims, making insurers financially better off. This increases net savings from distance -based pricing and reduces the financial risks to insurers. Technical concerns can be addressed by implementing distance -based pricing pilot projects to obtain better information on feasibility, costs, consumer demand, travel impacts, crashes, and revenue impacts. This could begin on a relatively small scale, and if no major problems are found it could ramp up until all motorists are offered distance -based pricing. Distance -Based Vehicle Insurance; Technical Report Victoria Transport Policy Institute 6 Introduction When grocery stores price cucumbers by the piece, customers tend to pick the larger ones fi rst. When the same vegetables are priced by weight, smaller cucumbers tend to be picked first. A tender little cucumber may be a good value by the pound but not by the piece. This illustrates how different pricing units can affect consumers’ decisions. This report explores the feasibility of implementing distance -based motor vehicle insurance. Distance -based pricing converts insurance from a fixed cost into a variable cost with respect to vehicle travel. Thus, the more
feasibility of implementing distance -based motor vehicle insurance. Distance -based pricing converts insurance from a fixed cost into a variable cost with respect to vehicle travel. Thus, the more you drive the more you pay, and the l ess you drive the more you save. Distance -based insurance is justified on actuarial grounds, since the more a vehicle is driven the greater its chance of having crashes and claims, all else being equal. Under current pricing, when a motorist reduces mile age the resulting insurance cost savings are dispersed among premium payers or retained as profits by their insurer. Individual motorists perceive no direct insurance savings for driving less. With distance -based pricing insurance cost savings that resu lt when a motorist reduces mileage are returned to that individual driver. These are net benefits to society, not just economic transfers. Motorist Reduces Mileage  Reduced Crashes  Insurance Cost Savings Distance -based pricing returns to individual motorists the insurance cost savings that result when they drive less. It rewards motorists for reducing mileage and makes premiums more accurately reflect the insurance costs of each individual vehicle. Distance -based pricing provides a marginal financ ial incentive to reduce mileage, allowing individual consumers decide which miles, if any , to forego. Any vehicle -miles reduced consist of lower -value vehicle travel that motorists willingly give up in exchange for financial savings, representing a net con sumer surplus. Motorists who continue their current mileage are no worse off on average with distance -based pricing (excepting any additional transaction costs), while those who reduce mileage are better off overall. To the degree that motorists reduce mileage, and therefore crashes and insurance claims, the savings that result are net benefits to society, not just economic transfers. Distance -Based Vehicle Insurance; Technical Report Victoria Transport Policy Institute 7 Distance -based insurance pricing can provide many benefits:  Increase d actuarial accuracy. It makes premiums more accur ately reflect the insurance costs of an individual vehicle.  Increase d insurance affordability . It offers motorists a new opportunity to save money. Savings could to average $50 -100 annually per participating vehicle with some systems.  It can increase consu mer choice. Distance -based pricing can be optional, allowing individual motorists to choose the pricing system that offers them the greatest benefits.  By reducing vehicle mileage it can reduce congestion , road and parking facility costs, energy consumption and pollution emissions, and provide other benefits.  It can significantly increase road safety. When motorists reduce their annual mileage they reduce crash risk to themselves and to other road users.  It is progressive with respect to income. Most lower income motorists should save money, since they tend to drive their vehicles less than average and
risk to themselves and to other road users.  It is progressive with respect to income. Most lower income motorists should save money, since they tend to drive their vehicles less than average and are relatively price sensitive.  It reduces the need to rely on cross -subsidies from low -risk motorists to provide “affordable” unlimited -mileage insurance c overage for higher -risk motorists. There are also barriers and costs associated with distance -based pricing:  It requires insurers and brokers to change how they calculate premiums, develop new procedures, and modifying computer programs.  Most distance -based pricing systems increase transaction costs. Incremental costs range from less than $10 to more than $150 per vehicle -year, depending on system.  It makes premiums and insurance revenues less predictable. Motorists and insurers would not know total prem iums until the end of the insurance term.  It can introduce new financial risks to insurers. It is possible that mileage and premium income would decline more than crashes, or that crash risk may shift to fixed -priced vehicles.  It increases premiums for som e motorists, and may reduce commissions for some brokers.  It has mixed political support, and there may be opposition from some stakeholders.  Many people are skeptical of predicted benefits. What would be the consequences if gasoline were sold like auto mobile insurance? With gasoline sold by the car -year, vehicle owners would make one annual prepayment that allows them to pump unlimited fuel from their company’s stations. Prices would be calculated based on the average cost of supplying fuel to vehicles with similar user profiles. Unmetered fuel would cause a spiral of increased fuel consumption, mileage, and total vehicle costs, including externalities such as accident risk, congestion, pollution and infrastructure costs. Low mileage (particularly lower income) drivers would simply drop out of the system because their costs per mile would be excessive, leaving them with fewer travel options. Of course, above average fuel users would defend this system because they enjoy benefits. Such a price system wou ld be irrational. It is comparable to current insurance pricing. Distance -Based Vehicle Insurance; Technical Report Victoria Transport Policy Institute 8 Automobile Pricing Practices This section discusses how distance -based insurance would affect overall vehicle costs. Current Vehicle Insurance Pricing Figure 1 shows the distribution of mo tor vehicle expenses. Motorists typically consider only fuel, out-of-pocket parking and toll charges as variable expenses. A portion of vehicle depreciation and most repair costs are also related to mileage over the long term, but they seldom influence individual trip decisions. Premiums per insured vehicle average approximately $ 850 per vehicle -year in the U.S., or about $1, 360 annually per household. Registration and license fees average about $ 250 per vehicle -year. Figure 1
per insured vehicle average approximately $ 850 per vehicle -year in the U.S., or about $1, 360 annually per household. Registration and license fees average about $ 250 per vehicle -year. Figure 1 Typical Costs for Intermediat e Size Car1 Depreciation31%Short-Term Parking & Tolls4%Insurance21%Financing6%Fuel & Oil19%Tires3%Registration3%Maintenance13%Variable CostsFixed Costs This graph illustrates the major financial costs of an intermediate size automobile averaged over a 12 year operating life. Although fixed vehicle expenses have increased substantially during the last thre e decades, variable costs have decreased in real terms. As a result, variable costs as a portion of total costs have declined significantly, as indicated in Figure 2. This price structure gives motorists an incentive to maximize their mileage in order to “ get their money’s worth” on their large fixed expenditures. This is particularly true of high risk drivers who pay large premiums for unlimited -mileage coverages. DBVI reduces the need to subsidize high risk driver, instead they simply pay high per -mile pr emiums ( Wilson 2023) . 1 Based on Jack Faucett Associates, Cost of Owning and Operating Automobiles, Vans & Light Trucks, 1991 , Federal Highway Administration (Washington DC), 1992. Distance -Based Vehicle Insurance; Technical Report Victoria Transport Policy Institute 9 Figure 2 Variable Automobile Costs as a Portion of Total Costs2 0%10%20%30%40%1950 1960 1970 1980 1990Percentage of Total Vehicle CostsVariable Expenses Insurance The variable portion of vehicle costs declined from about 40% in 1950 to 20% in 1995. Insurance actuaries acknowledge that mileage is an important risk factor, but usually give it little weight as a rating factor because self -reported data are unreliable.3 Instead, less accurate, indirect indicators of mileage are used, such as vehicle type, commute distance, demographic and geographic factors. Insurers consider several objectives besides risk when developing price structures, including administrative convenience, and marketing factors. Prices are often set to attract desirable customers, such as those likely to purchase other insurance (vehicle, home, life, etc.). Regulators often require insurance companies to underprice high -risk drivers for the sake of affordability. As a result, some types of motorists pay far more than their average accident costs, while others pay far less. Insura nce Affordability and Uninsured Driving (Litman, 2004) Unaffordable insurance is considered a major problem, particularly because it contributes to uninsured driving. Many low -income motorists are forced to drive uninsured, since insurance would cost a sig nificant portion of their net income. This creates a cycle of uninsured driving, uninsured claims and higher premiums in lower -income communities.4 Higher -income motorists sometimes drive uninsured if they own a vehicle that is only used occasionally. Alth ough most jurisdictions mandate minimum
higher premiums in lower -income communities.4 Higher -income motorists sometimes drive uninsured if they own a vehicle that is only used occasionally. Alth ough most jurisdictions mandate minimum levels of coverage, these requirements are often ignored.5 But enforcement strategies can be effective. In British Columbia, less than 1% of crashes involve uninsured motorists due to the successful integration of ve hicle insurance and licensing 2 Facts and F igures 95 , Motor Vehicle Manufacturers Association, 1995, p. 58. 3 CAS, Foundations of Casualty Actuarial Science , 3rd Edition, Casualty Actuarial Society (Arlington; www.casact.org ), 1996, p. 35. Also see p. 242 and 250. 4 Patrick Butler, How Per -Car Premiums Induce Adverse Selection and Foster the “High -Risk-Driver” Theory , presented at the Annual Meeting of the American Risk & Insurance Association, August 2004; available at Cents Per Mile ( www.centspermilenow.org ). 5 12% of 1989 insurance claims involved uninsured vehicles. Tom Wenzel, Analysis of National Pay -as-you-Drive Insurance Systems and other Variable Driving Charges , Energy & Environment Division, Lawrence Berkeley Laboratory (Berkeley), July 1995, p. 29. Distance -Based Vehicle Insurance; Technical Report Victoria Transport Policy Institute 10 transactions. Vehicle owners must pay for insurance to obtain license tabs. This is more effective than simply requiring proof of insurance, which can be evaded with counterfeit documentation. Factors Influencing Insurance Pr ices Insurance is regulated to achieve several objectives, including financial security and responsibility (i.e., to insure that insurance companies will not become bankrupt and cover claims as required), equity and affordability. In general, insurance p rices are intended to be actuarially accurate, meaning that premiums reflect the insurance costs imposed by each policy. This is considered most equitable (consumers pay the costs they impose) and economically efficient (it gives accurate price signals, so consumers have an incentive to reduce risks). However, in practice other factors affect vehicle insurance pricing. Because mos t jurisdictions mandate insurance , affordability is a major issue. Cost -based pricing would require some categories of motorist s to pay several thousand dollars a year for basic converge, which would make insurance, and therefore legal vehicle ownership, unaffordable to some lower -income drivers. To address this problem, regulators require insurance companies to provide coverage t o higher -risk motorists at less than full costs, resulting in subsidies from lower -risk to higher -risk premium payers.6 Insurance pricing is also affected by marketing objectives. For example, insurance companies’ may underprice automobile insurance attra ct higher -income consumers who are likely to purchase other types of insurance, such as household coverage.7 As a result, premiums often overcharge lower -risk motorists (what actuaries call “cream”)
higher -income consumers who are likely to purchase other types of insurance, such as household coverage.7 As a result, premiums often overcharge lower -risk motorists (what actuaries call “cream”) and undercharge higher -risk motorists. This results in ex tremely high premiums in lower -income areas, since a greater portion of low -mileage motorists drive uninsured which reduces funds to cross -subsidize higher -mileage motorists.8 As explained by the National Organization for Women’s Insurance Project,9 “Compu lsory insurance seems to work in upper -income zip codes where most people can afford to keep insurance on cars driven less than average. Because these cars cost insurers proportionately less in claims, they bring in extra profits and insurers privately cal l landing their business “skimming the cream.” Insurers use extra profits from “cream” customers to compete by holding car insurance prices down for their preferred customers who have many other insurance needs. Customers typically skimmed and overcharged are those who commute by carpool, bus or bicycle, and also women, older people, and households with more cars than drivers. In low income zip codes, insurers redline many cars to higher “nonstandard” prices —not because their drivers are less careful, as in surers encourage everyone to believe —but because of the scarcity of “c
EXPLORING THE IMPACT OF E-INSURANCE AS A DISTRIBUTION PLAT FORM TO IMPROVE SALES OF THIRD-PARTY MOTOR INSURANCE IN NIGE RIA. BY OMOTAYO BALOGUN IN FULFILMENT FOR THE AWARD: MSc. INTERNATIONAL MANAGEMEN T (DIGITAL BUSINESS) APPLIED. TEESSIDE UNIVERSITY May, 2024. 1 ABSTRACT The global expansion of the automobile industry has heralded new opportu nities for the insurance sector; however, developing countries like Nigeria have yet to fully capitalize on this growth. Nigerian insurance companies struggle with the challenge of i mplementing innovative business models to address issues of transparency, consumer confidence, di stribution, sales, penetration, and financial inclusiveness, particularly within the domain of third-party motor insurance. This study emphasizes the critical need for insurance compan ies to integrate technology with their business models, leveraging digital solutions to bridge the su bstantial gap between the number of vehicles on Nigerian roads and the number of insured vehicles. Th rough the adoption of e-insurance platforms, insurance firms stand to broaden their market reach, improve accessibility, optimize distribution channels, augment sales figures, and foste r healthy competition within the industry. Employing qualitative research methodologies, inc luding semi-structured interviews with both consumers and insurance practitioners, this thesis in quires deep into the exact attitudes of consumers, the valuable understanding from industry professionals, and t he evolving dynamics of Nigeria's insurance industry. The research findings present a comp rehensive understanding of consumer perspectives and industry insights, offering actionable recommendations for insurance stakeholders to navigate the evolving terrain of third-party m otor insurance in Nigeria. By harnessing the transformative power of e-insurance platforms and al igning technology with strategic objectives, insurance companies can unlock new avenues for growth, stimulate innovation, and drive sales and sustainable development within N igeria's dynamic insurance sector. 2 CHAPTER ONE 1.0 Introduction of the Study The motivation behind this study originates from the pressing desire to address the significant challenges facing the Nigerian insurance industry in this digital era. With the swift evolution of Internet technology and changing consumer expectations, there is a clear imperative for insurers to adapt and innovate to remain competitive. E-insurance, as a manifestation of this digital transformation, offers immense potential to revolutionize the way insurance products and services are distributed and accessed. However, despite its promise, th ere remains a notable gap in the adoption of e-insurance platforms, particularly in the context of t hird-party motor insurance sales. By exploring the impact of e-insurance on the sales of third-party moto r insurance in Nigeria, this study seeks to uncover possibilities that can inform strategic interventions and
insurance sales. By exploring the impact of e-insurance on the sales of third-party moto r insurance in Nigeria, this study seeks to uncover possibilities that can inform strategic interventions and drive the industry toward greater efficiency, accessibility, and customer sati sfaction. Through a deeper understanding of consumer attitudes, industry perceptions, and best practices in digi tal distribution, this research aims to pave the way for a more resilient and responsive insuran ce sector in Nigeria. 1.1 Structure of The Study This study will be structured into several key sections to c omprehensively address the research objectives and questions. The first section will focus on the background of the study, outlining the background, context, and significance of investigating the impact of e -insurance on third-party motor insurance sales in Nigeria. Following this, a thorough revi ew of relevant literature will be presented, covering topics such as digital transformation in the insura nce industry, the emergence of e-insurance, and factors influencing consumer behavior. Subseque ntly, the methodology section will detail the research approach, design, data collection m ethods, and analytical techniques employed in the study. The findings of the research will then be p resented and analyzed, drawing upon understandings gained from interviews, and other data sources. Fina lly, the study will conclude with a discussion of the implications of the fi ndings, their relevance to theory and practice, and potential avenues for future research in the fiel d of e-insurance and motor insurance sales. 3 1.2 Background of Study The rise of Internet technology has profoundly influenced consumer beh avior and expectations across diverse industries. In the present day, consumers desi re more than merely competitive pricing and high-quality products or services. They prioritize compan ies capable of providing swift services, easy accessibility, efficient outreach, and conveni ence that align seamlessly with their fast-paced lifestyles. E-insurance refers to the utilization of online platforms for t he sale, delivery of services, and dissemination of information related to insurance (Sapa et al., 2014). This encompasses the application of the Internet and associated information techno logies for the provision and circulation of insurance services, involving processes such as solicitation, negotiation, contracting, and the online distribution of insurance policies (Sergey, 2016). The advent of digital technology has transformed the distribution of insurance services, emerging a s a fundamental factor in the success of individuals and businesses across diverse sectors . The utilization of the internet, mobile devices, telematics, and social networks has brought about a profound shift in how insurers engage with their clientele. This evolution empowers customers wi th increased access to information regarding their risk exposures, fostering a trend toward greater
a profound shift in how insurers engage with their clientele. This evolution empowers customers wi th increased access to information regarding their risk exposures, fostering a trend toward greater s elf-reliance in meeting their insurance requirements (Hung 2020). Leveraging digital technologies, platforms, and infrastructures for innovation presents entrepreneurs with the chance to introduce novel products, serv ices, and improved processes across various industries (Gault 2018; Nambisan et al. 2019). The insurance sector is no stranger to this trend, as innovation is intricately tied to emerging t echnologies and encompasses the entire value chain (Bohnert et al. 2019; Eling and Lehmann 2018). Advanced nations have already embraced digital products within t he insurance sector, capitalizing on modern data channels, improved data processing capacities, and advancements in Artificial Intelligence algorithms (Aggrey et al., 2012). However, insurance service providers in developing countries such as Nigeria encounter substantial challenges in ke eping pace with their counterparts in countries like India, the USA, and the UK. This is because they are not leveraging the available 4 technology platforms to develop innovative touchpoints and provide customer-friendly experiences. Advancements in technology have transformed the way insurance se rvice buyers access information about products and services (Chatterjee et al., 2002). The internet has made it easier for customers to access information, and modern technologies tha t enable quick and efficient comparison of propositions have increased the demand for bett er insurance products. The amalgamation of digital technology and innovative thinking offer s substantial prospects for the distribution and sales of motor third-party insurance. This encom passes leveraging mobile and web technologies to boost sales online, along with inventive mo dels of distribution (Seitz, 2017). Transforming Nigeria's insurance market to increase sales and dis tribution agility for motor third-party Insurance could be achieved by crafting new business models that address the requirements of drivers in both urban and rural areas (Barkur, Rodrigues, and Varambally, 2 007). The use of information technology in the motor insurance sector has the pot ential to transform the way insurers and customers interact. It can be leveraged to in crease sales and enhance distribution strategies. Third-party liability insurance plays a vital role in assi sting vehicle owners in covering financial responsibilities arising from harm or injury to third partie s, particularly in developing nations with a significant number of low-income individuals (Marso n, Nicholson, and Ferris, 2017). Despite compulsory insurance coverage for vehicles in Nigeria, over 71.7% of cars have no access to insurance, and manual selling is more prevalent than techno logy-driven selling. Integrating e-insurance into product distribution channels can benefit the
over 71.7% of cars have no access to insurance, and manual selling is more prevalent than techno logy-driven selling. Integrating e-insurance into product distribution channels can benefit the Ni gerian insurance industry significantly. The prospect of an e-insurance-enabled insurance platform is appealing to many in the industry, and the advantages of reduced transaction costs, more competitive products, and expansion of markets cannot be overemphasized (Fisher, 2009; McCarthy, 2000). India and Nigeria, both characterized by sizable populations, exhi bit distinct trends in their insuran sectors. In India, the insurance sector has warmly embraced e-insur ance, with motor insurance emerging as the leading contributor to business among vario us general insurance products. As per the Indian Brand Equity Foundation (IBEF), a governmental entit y, motor insurance commanded 5 a substantial 36.60 percent market share within the realm o f general insurance products in India during FY20 (cited in Manoj, 2020). The insurance industry in India is progressi vely integrating Information Technology for tasks such as process automation and cos t reduction. This shift necessitates efficient handling of substantial data volumes, em phasizing the imperative for insurers to adopt a data-driven approach and leverage data to their strategic a dvantage. Digital technologies have the potential to transform various operational aspects that affect both insurers and customers and improve insurance sales if strategica lly developed in the Nigerian insurance industry. While many researchers have talked about e-insurance, few have examined the role of e-insurance as a sales and distribution platform to improve s ales of third-party motor insurance in Nigeria. This research uses qualitative methods to explore the role of e-insurance distribution platforms on the sales of third-party motor insurance in Nigeria . 1.3 Statement of the Problem Motor insurance is one of the six compulsory insurance policies in Nige ria, and it is widely used in the country. With a population of over 226.2 million, of which almos t 70% are young people, there is a huge potential for growth in insurance and financial s ervices in Nigeria. However, despite these opportunities, the insurance industry in the country is still st ruggling to thrive. The contribution of the industry to the nation's gross domestic product is less than 1%, and only 3.4 million people have motor insurance coverage in Nigeria according to NIA 2022. Numerous experts assert that the Nigerian insurance sector has bee n sluggish in embracing digital technologies, thus failing to fully harness the potential of di gitalization (Müller et al., 2015, as cited in Martin 2020). Nevertheless, a prevailing viewpoint a mong market participants is that digitalization holds the promise of fundamentally reshaping the value-creation dynamics of the industry. This transformation is anticipated to usher in nov el modes of customer interaction,
is that digitalization holds the promise of fundamentally reshaping the value-creation dynamics of the industry. This transformation is anticipated to usher in nov el modes of customer interaction, innovative business processes, fresh risks, and advancements in pro duct technologies (Catlin, Hartmann, Segev, & Tentis, 2015). Despite the surge in interes t globally due to recent advancements in insurtech, academic discourse on digitalization' s impact on the insurance sector, particularly in the context of third-party motor insurance sale s, remains relatively scant. This research study therefore explores the impact of e-insurance as a distribution platform to improve the sales of third-party motor insurance in Nigeria. 6 1.4 Aims of the Research. This study aims to understand the Impact of E-Insurance as a distribution Platform to Improve Sales of third-party motor insurance in Nigeria. 1.4.1 Objectives of the Research  To understand the attitude and perceptions of consumers towa rds E-Insurance as a platform for third-party motor insurance.  To identify the factors that influence consumers' trust and confidence in purchasing third-party motor insurance through E-Insurance platforms.  To understand the viewpoints of insurance industry practitioners on t he prospective benefits and disadvantages of integrating E-Insurance into the sales of third-party motor insurance.  To make suggestions and recommendations for using E-Insurance as a distribution platform to improve the sales of third-party motor insurance in the Ni gerian market. 1.5 Research Questions What is the Impact of E-Insurance as a distribution Plat form on Sales of third-party motor insurance in Nigeria? 1.6 Significance of the study The significance of this study cannot be overstated. Motor insur ance is a compulsory insurance product in Nigeria that is meant to be purchased by every motorist. However, it is unfortunate that 71.7% of vehicles in Nigeria are still uninsured. E-insurance has been successful in generating sales of this product in other developing nations like India to expa nd the insurance net and bring customer-oriented experience to the insuring public. This researc h is timely as the insurance industry in Nigeria is seeking a major transformation to increas e the sales of third-party motor insurance. As this study probes into the literature review chapter, it wil l explore existing studies and perceptions related to e-insurance adoption, particularly in the context of motor insurance, shedding light on benefits, disadvantages, its use as a distribut ion platform, and lessons from comparable contexts such as India and how technology has been used to driv e efficiency. 7 1.7 Rationale Behind the Study The rationale for conducting this study arose from the urgent need to address the challenges facing the Nigerian insurance industry, particularly in the contex t of third-party motor insurance sales. Despite being a compulsory insurance product, a significant porti on
address the challenges facing the Nigerian insurance industry, particularly in the contex t of third-party motor insurance sales. Despite being a compulsory insurance product, a significant porti on of vehicles in Nigeria remains uninsured, posing financial risks to both vehicle owners and third pa rties. E-insurance has emerged as a potential solution to enhance the accessibility, effici ency, and effectiveness of insurance distribution channels, yet its impact on third-party motor insurance sales in Nigeria remains understudied. By investigating the role of e-insurance as a distribut ion platform, this study aims to fill this knowledge gap and provide a valuable report that can inform strategies to improve the sales and distribution of third-party motor insurance in Nigeria. Such reports are crucial for the industry's efforts to expand insurance coverage, mitigate r isks, and contribute to the overall socio-economic development of the country. 1.8 Definition of Terms Risk: This is a situation of being exposed to danger or the possibili ty that something unexpected, or unpleasant may occur. Insurance: Insurance is like a safety plan. You pay a little money (premiu m) to a company (insurer), and they take on some or all of the risk if something bad ha ppens to you or your property. ROI: return on investment E-insurance refers to using the Internet and related information technologie s to provide and distribute insurance services. 1.9 Research Design The research design for this study will adopt a qualitative app roach, employing methods such as interviews, journals, and other data in the public domain, a nd content analysis. Firstly, semi-structured interviews will be conducted with key stakeholders li ke insurance practitioners anonymously to gather their perspectives on the role of e-insurance in third-party motor insurance sales. These interviews will provide an in-depth understanding of t he challenges, opportunities, and potential strategies for leveraging e-insurance platforms to improve sales and distribution. 8 Secondly, interviews will be organized with consumers of third-part y motor insurance to explore their attitudes and behaviors regarding e-insurance platforms. These disc ussions will facilitate a deeper understanding of consumer perceptions, trust factors, and de cision-making processes when purchasing insurance through digital channels. Lastly, thematic analysis will be employed to analyze releva nt literature, industry reports, and online discussions related to e-insurance and third-party motor insurance sales in Nigeria. This will provide a comprehensive overview of existing research, industry trends, and best practices, which will inform the interpretation of findings from the interviews. Overall, this qualitative research design will enable a holis tic exploration of the research questions, revealing the complex dynamics of e-insurance distribution and its impact on third-party motor insurance sales in Nigeria. 1.9.1
design will enable a holis tic exploration of the research questions, revealing the complex dynamics of e-insurance distribution and its impact on third-party motor insurance sales in Nigeria. 1.9.1 Research Structure Introduction: This section will provide an overview of the research topic, including background information, the rationale for the study, research questions, aims, o bjectives, and significance of the research. Literature Review: This section will review relevant literature related to e-in surance, digital technology in the insurance sector, third-party motor insurance, and c onsumer behavior. It will explore existing research, theories, and concepts to provide a t heoretical framework for the study and identify gaps in the literature. Research Methodology: This section will outline the research design, including details of the qualitative methods approach, data collection methods (intervie ws), sampling techniques, data analysis procedures, and ethical considerations. Findings and Analysis: This section will present the findings of the study, includ ing qualitative interview perspective and results. It will analyze the data to address the research interview questions and objectives, identifying patterns, themes, and relationshi ps. Conclusion and Recommendations: This final section will summarize the key findings of the study, discuss their implications for theory and practice, and pro vide recommendations for 9 stakeholders in the Nigerian insurance industry. It will al so highlight the limitations of the study and suggest areas for future research. Reflective Statement: This section serves as evidence of the researcher's active i nvolvement in the dissertation process and showcases the growth and enhancement of the skills and knowledge throughout the endeavor. 10 CHAPTER TWO LITERATURE REVIEW 2.0 Introduction The literature review will explore a wide array of topics and conce pts related to e-insurance, technology adoption in the insurance industry, consumer behavior, and the sal es and distribution of third-party motor insurance. Specifically, it will touch on e-insur ance and its impact as an insurance distribution platform. Concepts such as technology adoption, i nnovation in insurance, customer-centric approaches, and technological advancements will be discussed to provide a comprehensive understanding of the subject matter. Additionall y, theories and frameworks related to consumer behavior, trust, and adoption of digital platforms will be examined to shed light on the factors influencing consumers' attitudes and perception s towards e-insurance. Moreover, the literature will review qualitative empirical data on e-insura nce adoption in both developed and developing countries to draw insights and lessons applicable to the N igerian context. Overall, the literature review will provide a robust body of knowledge that i nforms the research study on the impact of e-insurance as a distribution platform for motor third-party i
context. Overall, the literature review will provide a robust body of knowledge that i nforms the research study on the impact of e-insurance as a distribution platform for motor third-party i nsurance in Nigeria. 2.1 Literature Review Strategy A narrative literature review approach was chosen for this stu dy due to its flexibility and suitability for exploring evolving research areas such as e-insurance and digital technology adoption in the insurance sector. Unlike systematic reviews, which follow a stric t protocol and aim to answer specific research questions, narrative reviews allow for a more organi c exploration of diverse literature sources, enabling the researcher to develop a ref ined understanding of the topic (Green et al., 2006). In contrast to scoping reviews, which aim t o map out the existing literature and identify research gaps, narrative reviews explore deeper into sel ected themes and concepts, providing detailed exploration and interpretations (Grant and Boot h, 2009). The narrative review strategy employed in this study involves a comprehensive exami nation of various types of literature, including academic articles, industry reports, and empirical research in a qualitative approach, to explore the evolution of digital technology, e-insura nce, e-insurance benefits and disadvantages, e-insurance as a distribution platform, cons umer behavior dynamics, and the role of e-insurance as a distribution channel. By synthesizing diver se sources of literature and utilizing 11 theoretical frameworks like the Technology Acceptance Model (TAM) and t he Unified Theory of Acceptance and Use of Technology (UTAUT), this narrative review aims to provide a valuable understanding of the factors influencing the adoption and effect iveness of e-insurance platforms in Nigeria's insurance industry. 2.1.1 Digital Technology The evolution of information technology, telecommunication, and the expa nsion of internet and wireless communication technologies is reshaping the financial se rvices sector, particularly the insurance domain. These technological strides empower ins urance companies and agents to enhance service delivery and cost savings for consumers. Digital technology facilitates quicker, more cost-effective, and reliable handling and sharing of informati on compared to historical practices (Nyangosi, 2011). Hebber et al. (2014) emphasize that the technological environme nt in developing nations is undergoing rapid transformations, often outpacing developments in more a dvanced counterparts. To thrive, businesses in these regions must prioritize ke y drivers, such as identifying and efficiently implementing new market opportunities, enhancing the value of existing customer relationships to foster long-term loyalty, and innovating to streamline cust omer interactions, irrespective of geographical constraints. 2.1.2 E-Insurance E-insurance encompasses online platforms that offer insurance sales, se rvices, and information. It is a broad term
cust omer interactions, irrespective of geographical constraints. 2.1.2 E-Insurance E-insurance encompasses online platforms that offer insurance sales, se rvices, and information. It is a broad term describing the use of the Internet and related inf ormation technologies (IT) in creating and delivering insurance services. In a more specific c ontext, it refers to the offering of insurance coverage where policies are solicited, negotiated, pre sented, and contracted on the Internet (Sapa et al., 2014). E-insurance involves leveraging technology to deliver insurance services and meet the needs of clients on a global scale (Saee d, 2012). E-insurance is the process of modernizing insurance services t hrough the adoption of new technologies, simplifying insurance policies, and enhancing competiti ve advantages. It signifies the evolution of insurance into electronic formats, with Insurt ech representing the future of the industry (Radwan, 2018). 12 According to Ahonen and Jarvinen (2003), e-insurance entails providing i nsurance services more efficiently by using electronic channels. E-insurance is defined by Morsi (2016) as a process that facilitates, advertises, and bargains for insurance services onl ine. E-insurance, to put it simply, is the process of creating and employing an information infrastructure and developing and putting into effect the policies, guidelines, and procedures required to c arry out digital or information society operations in the insurance industry (Hatami, 2005, p. 1 5). Manual insurance operations are replaced by e-insurance (Meshkat et al., 2012). Insurance companies in Nigeria can use E-Insurance to improv e efficiency, lower costs, increase sales, and create new products and services. The creation of t he internet and related electronic devices has made it simpler and more convenient to provide fi nancial services to customers at a reduced cost. Customers can now easily purchase third-party motor in surance through an efficient online process, leading to higher sales volume. This chapter revi ews past literature on e-insurance and explores ideas about the impact of e-insurance on the sales of third-party motor insurance. 2.2 Benefits or Advantages of E-insurance: Mohamed, O.A., (2020) in a journal titled E-Insurance Concept, Importance, and Applications stated that applying e-insurance technologies brings several signifi cant opportunities and advantages such as: 1. Minimizing unnecessary expenses Promoting insurance services online offers cost and time a dvantages over traditional advertising practices. Additionally, automating insurance services can c ut administration costs and enhance the management of customer databases. The cost-efficiency of e-insuran ce may result in lower insurance premiums, potentially inspiring customers to buy more insurance. 2. Assisting in broadening the target market Transitioning into a digital system enables insurance companie s to broaden their reach and enter new markets
inspiring customers to buy more insurance. 2. Assisting in broadening the target market Transitioning into a digital system enables insurance companie s to broaden their reach and enter new markets encompassing diverse cultures, age groups, and social d emographics. 3. Gaining a Competitive Edge: In today's digital age, customers conduct their daily activities online, and it includes buying, selling, and exchanging products and services. Consequently, insurance fi rms that adopt and 13 provide online services, simplifying processes to be more effic ient, rapid, and cost-effective, secure a competitive edge. 4. Enhancing Service Quality: E-insurance empowers insurance companies to elevate the qualit y of their services. It enables companies to deliver faster and easily accessible service s, thereby fulfilling a broader range of customer needs and ensuring satisfaction. 2.2.1 Challenges of E-Insurance Mohammed (2020) has pointed out some limitations of e-insurance. A ccording to him, technical hurdles can make it hard to ensure the reliability and security of the network used. In addition to that, the limitation of specialized networks also poses a rest riction to e-insurance (Hiwarkar, 2013). Pandey (2012) has emphasized that the primary impediments hinderi ng the progress of the e-insurance sector include the absence of systematic planning and net working technologies, a shortage of skilled human manpower (such as surveyors, actuaries, loss adjusters, and loss assessors), and a general lack of adequate attention among bot h the public and insurance firms regarding the advantages of e-insurance. 2.3 E- Insurance as a Distribution Platform Different ideas surrounding the distribution of insurance products have been explored in academic literature. However, limited focus has been directed towards an in-dep th examination of these concepts. Yu. Klapkiv, for instance, clarified the importan ce of mobile technology solutions as a platform for online service distribution and defined "distribution" a s the transfer of commodities and services from producers to consumers (Klapkiv et al., 2018) . Pikus and Zakolodyazhnyi (2016) conducted research and expressed interest in novel and inventive dist ribution methods for insurance products, especially in the personal insurance market. Insurance companies should focus on developing digital channels t o boost the sales of their insurance products, especially third-party motor insurance, which is compulsory insurance. Pousttchi (2019) and Porrini (2018) asserted that insurance entitie s ought to concentrate on crafting customer-centric business models and hybrid service-oriented, susta inable, and inventive digital 14 products, and collaborations with Insurtech and technology firms to e nhance the digitization of distribution channels. Customer preferences are dynamic, and an effective strategy to cater t o their third-party insurance requirements involves establishing a digital distribution platform . In the
distribution channels. Customer preferences are dynamic, and an effective strategy to cater t o their third-party insurance requirements involves establishing a digital distribution platform . In the research paper titled "The Future of Insurance Intermediation in the Age of the Digital Pl atform Economy," Stricker et al. (2023) inquire into the implications of multi-sided platforms on i nsurance intermediation. The study observes that the intersection of digitalization and evolv ing customer preferences has given rise to Insurtech enterprises and multi-sided platforms. These plat forms exhibit enhanced capabilities in terms of agility, scale, and scope, and th e paper examines their prospective role in the realm of insurance intermediation. Presently, third-party motor insurance services in Nigeria are mostly traditionally distributed through internal and external channels. External channels encompass age nts, brokers, and banks (bancassurance), while direct sales to insurers constitute the int ernal channels, proving more lucrative for insurance firms as they eliminate commission fees. In recent years, technology has been harnessed to enhance the efficiency of agents and brokers in d istribution. The advent of the internet, the rise of e-commerce, and the widespread accepta nce of online transactions have prompted insurance companies to leverage technology, utilizing webs ites for selling third-party motor insurance. However, challenges such as technology adoption, illiteracy, and low financial inclusion among the unbanked have impeded sales growth and in clusion. Addressing these challenges necessitates acknowledging the pivotal role of internet ac cess, a prerequisite for deploying a technology-driven platform that can facilitate and brid ge the gap of accessibility of motor third-party insurance from any location. (Aroro, 2013) mentioned channels in e-insurance, and they are highlighted be low: 1. Internet Marketing The rapid growth of the internet has sparked debates about its potential impact on traditional distribution channels. In India, for example, although there is a growing number of internet users, online transactions for insurance services are still not widely adopt ed due to security concerns. While some companies provide insurance services online, it is still a minute part of the overall insurance distribution system. 15 Currently, the majority of insurance companies have product details and educational resources available on their mobile apps and websites.. However, these serv ices are not viewed as a means for direct selling of insurance products and services. In Nige ria, India, etc., where insurance is still sold through face-to-face interactions, selling over the Internet is not yet a popular option. Although the internet is being used as a support channel, its adopt ion rate as a distribution channel has been slow. In countries like Nigeria and India, where internet penetration is still low and there are legal issues with
used as a support channel, its adopt ion rate as a distribution channel has been slow. In countries like Nigeria and India, where internet penetration is still low and there are legal issues with online agreements, the insecurity associated with internet tra nsactions remains a significant challenge. For now, the internet has not evolved into an effective mea ns for the direct selling of insurance products and services. 2. User-Based and User-Focused Technologies: User-Based and User-Focused Technologies refer to technologi es that cater to the needs and preferences of customers. In today's world, where customers prefer to shop online, insurance companies have to change the way they do business. The ease of browsing the internet and comparing deals online has made online shopping the most pop ular mode of shopping. The use of mobile devices for payment is also gaining acceptance. 3. Self-driving cars: The imminent availability of self-driving cars necessitate s preparation within the insurance industry for this driverless future. These vehicles utilize advanced software to analyze real-time data and model the behavioral dynamics of surrounding drivers, pe destrians, and objects. The learning algorithm incorporates data not only from the autonomous vehicle itself but also from others nearby, determining appropriate responses to potential issues. T he anticipated reduction of accidents by 90% with the advent of self-driving cars will have a profound impact on auto insurance pricing and the processing of claims. 4. Robotics/Process Automation: The insurance industry is rapidly adopting chatbot technol
383ACTA UNIVERSITATIS AGRICULTURAE ET SILVICULTURAE MENDELIANAE BRUNENSISVolume 62 41 Number 2, 2014GENERALIZED LINEAR MODELS IN VEHICLE INSURANCESilvie Kafková1, Lenka Křivánková21 Masaryk University , Faculty of Economics and Administration, Lipová 41a, 602 00 Brno, Czech Republic2 Masaryk University , Faculty of Science, Kotlářská 2, 611 37 Brno, Czech RepublicAbstractKAFKOVÁ SILVIE, KŘIVÁNKOVÁ LENKA. 2014. Generalized Linear Models in Vehicle Insurance. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 62(2): 383–388.Actuaries in insurance companies try to ﬁ nd the best model for an estimation of insurance premium. It depends on many risk factors, e.g. the car characteristics and the proﬁ le of the driver. In this paper, an analysis of the portfolio of vehicle insurance data using a generalized linear model (GLM) is performed. The main advantage of the approach presented in this article is that the GLMs are not limited by inﬂ exible preconditions. Our aim is to predict the relation of annual claim frequency on given risk factors. Based on a large real-world sample of data from 57 410 vehicles, the present study proposed a classiﬁ cation analysis approach that addresses the selection of predictor variables. The models with diﬀ erent predictor variables are compared by analysis of deviance and Akaike information criterion (AIC). Based on this comparison, the model for the best estimate of annual claim frequency is chosen. All statistical calculations are computed in R environment, which contains stats package with the function for the estimation of parameters of GLM and the function for analysis of deviation.Keywords: vehicle insurance, generalized linear model, poisson distribution, link function, analysis of deviance, Akaike information criterion1 INTRODUCTIONActuarial science is a dynamically developing ﬁ eld dealing with an assessment of risk in insurance. Vehicle insurance is an insurance designed for cars, trucks, motorcycles, and other road vehicles. It is used to provide ﬁ nancial protection against the damage of the vehicle and a bodily injury resulting from traﬃ c collisions. Moreover, it hedges against the liability which could arise in a traﬃ c accident. The speciﬁ c terms for vehicle insurance and its type vary with legal regulations. A review of actuarial modeling in vehicle insurance is given in Denuit (2007).The process, by which insurers determine whether to insure an applicant and which premium to charge, is called vehicle insurance risk selection. The insurance premium is usually derived from an annual frequency of claims, which is modeled by using statistical data. This approach for computation of the premium can be found in Kaas (2009) and Ohlsson and Johansson (2010). The annual frequency of the claims is calculated from the number of the claims on a contract. They depend on many factors that are believed to have an impact on the expected cost of future claims. Those factors can include the car
is calculated from the number of the claims on a contract. They depend on many factors that are believed to have an impact on the expected cost of future claims. Those factors can include the car characteristics (vehicle body , vehicle age) and the proﬁ le of the driver (age, gender, driving history). Based on the idea of Heller and Jong (2008) and Kaas (2009), we develop models for the vehicle insurance.The number of claims is a random variable. Based on Pearson’s chi-squared test we assume that the number of claims on a contract is Poisson distributed.Policyholders are divided into several tariﬀ groups. For each group, generally diﬀ erent expected values of claims are assumed. The expected value of a Poisson distributed random variable is equal to its variance. Because such expected values in individual groups are diﬀ erent, it leads to the occurrence of heteroskedasticity . Therefore, we cannot usethe classical linear regression model.The expected value of the random variable with the Poisson distribution is always positive. Under the assumption that the mean depends linearly 384 Silvie Kafková, Lenka Křivánkováon the explanatory variables, its positivity cannot be guaranteed. Therefore, logarithmic transformation guaranteeing the positivity is used. In such case, instead of obtaining an additive model we get a model with a multiplicative eﬀ ect on the mean.These are the reasons that lead us to use generalized linear models (GLMs). In particular, we use GLM with the Poisson distributed response variable and with the logarithmic link function. Generalized linear models became very popular since their introduction in Nelder and Wedderburn (1972), primarily due to the ability to handle discrete data via an extension of the familiar Gaussian regression model to the models based on underlying exponential family of distributions. A basic notation, deﬁ nition and framework of GLMs are described e.g. in Dobson (2002). For the wide overview on GLMs see the standard text McCullagh and Nelder (1989).The aim of this paper is to develop a suitable model for an annual frequency of claims. Based on this model, the actuary can determine an adequate insurance premium for each group of drivers. The analysis of deviance and the Akaike information criterion are used for comparison of the examined models.Over the last years generalized linear models became a favorite statistical tool to model actuarial data. We refer to Haberman and Renshaw (1996) for an overview of applications of GLMs in actuarial science. For example, Gschlössl, Schoenmaekers and Denuit (2011) described the application of GLM for a construction of life tables in life insurance. Another application of GLMs in life insurance is introduced in Cerchiara, Edwards and Gambini (2008), where GLMs are used in context of lapse risk as a mean to understand the relationship between risk factors and to calib rate the lapse risk as accurately as possible. Advantages of the GLMs approach are discussed in
in context of lapse risk as a mean to understand the relationship between risk factors and to calib rate the lapse risk as accurately as possible. Advantages of the GLMs approach are discussed in Antonio and Beirlant (2007). Furthermore, they presented the usage of generalized linear mixed models in actuarial mathematics.The insurance portfolios have very speciﬁ c characteristics, because, for many policies, there are no claims observed in the insurance history for a given period. It means that the data contains lots of zeros and therefore the GLMs may not give satisfactory results. This common situation considering the insurance data is discussed in Wolny-Dominiak (2012).2 MATERIALS AND METHODSThe most common approach for modeling the relationships between variables uses linear regression models. A disadvantage of the standard linear regression model is the assumption of normally distributed observations, which does not allow appropriate modeling of counts, frequencies, binary or skewed data.Another assumption of the linear regression models is that the mean of observations is a linear function of the parameters. Accordingly , it permits only additive models but not multiplicative ones. Moreover, linear regression models assume an independence of the variance and the mean while the variability o/ft en increases with the mean value in real data.If the data does not comply to the above mentioned properties of linear regression model, we can use generalized linear models which do not require such strict assumptions.2.1 Generalized Linear ModelsIn this section, we give only summary of the main characteristics of generalized linear models (GLMs). For a broad introduction to the generalized linear models, we refer to McCullagh and Nelder (1989), Dobson (2002) and Hardin and Hilbe (2007). Main attributes of the GLMs are the generalization of probability distribution of the dependent variable and giving a possibility to transform the data.GLMs extend the framework of linear regression models with normal distribution to the class of distributions from the exponential family . It allows modeling of large numbers of types of variables (counts, frequencies, etc.) and to treat skewed probability distributions of the data, too. Densities from the exponential family are deﬁ ned in the following canonical form.Deﬁ nition 1. The set of probability density functions (p.d.f.) written of the form ()() =(,) e x pyafy cy is called the exponential family , where θ and ϕ are parameters, θ is called the canonical parameter or the scale parameter and ϕ the dispersion parameter. a( θ) and c(y, ϕ) are known functions determining the actual probability function such as Binomial, Poisson, Normal or Gamma. Further generalization uses a link function which allows to model transformed data. The link function makes a connection between the mean and a linear function of the explanatory variables. A transformation of the mean is modeled as a linear function of
to model transformed data. The link function makes a connection between the mean and a linear function of the explanatory variables. A transformation of the mean is modeled as a linear function of explanatory variables.Deﬁ nition 2. The link function g (μ) is a monotonic diﬀ erentiable function of the form g(μ) = x'β,where β is the vector of regression parameters and x is a vector of the explanatory variables. The link function g(μ) determines how the mean is related to the explanatory variables x. Common link functions g(μ) are given in the T ab. I, in relation with speciﬁ c probability distributions of the data. Generalized Linear Models in Vehicle Insurance 385Deﬁ nition 3. Let Y be a random variable with mean denoted by μ and p.d.f. from the exponential family . Then the generalized linear model (GLM) is given by g(μ) = x’β,where g(μ) is the link function. The generalized linear models provide relatively simple and robust way to analyze the eﬀ ect of many diﬀ erent factors on some observed event. The GLMs are used for valuation of insurance policies due to the number of claims. In GLM, it is assumed that the number of the claims is a dependent variable which follows Poisson distribution and which depends on known predictors. The predictors characterize the insured individual or vehicle, e.g. gender, age, engine capacity .2.2 Methods of Comparing Diﬀ erent ModelsDetermining appropriate model is the basis of regression modeling. One important principle of regression modeling is the principle of simplicity . The simpler model, well describing the data, gets priority over the more complex model that describes the data almost perfectly .2.2.1 Analysis of Deviance Along with the basic generalized linear model, we also take into account the following partial models, which are called submodels.Deﬁ nition 4. The full model , denoted as GLMmax, satisﬁ es the following conditions: • it has the same distribution as the proposed model, • it has the same link function as the proposed model, • the number of parameters is equal to the number of the response variables. The response variables are determined by the full model with residues equal to zero.Deﬁ nition 5. The null model , denoted as GLMmin, satisﬁ es the following condition: • it has the same distribution as the proposed model, • it has the same link function as the proposed model, • the number of parameters is equal to one. The full model is an indicator of the “best regression” and the null model gives the “worst regression” with given distribution and link function. The proposed model will be somewhere between these two extreme models. The relevance of the proposed model will be evaluated via comparison with these models. However, such comparison is permitted only for the original model and its submodel.Deﬁ nition 6. Consider GLM with design matrix Xn×m and vector of parameters βm. Its submodel , denoted as GLMsub, with design matrix Qn×q and vector of parameters βq satisﬁ es the following
submodel.Deﬁ nition 6. Consider GLM with design matrix Xn×m and vector of parameters βm. Its submodel , denoted as GLMsub, with design matrix Qn×q and vector of parameters βq satisﬁ es the following conditions: • it has the same distribution as the proposed GLM, • it has the same link function as the proposed GLM, • the number of parameters is q < m and columns of the design matrix Qn×q are linear combinations of columns of the design matrix Xn×m. The deviance is deﬁ ned as a measure of distance between the full model and the proposed submodel.Deﬁ nition 7. The deviance , denoted as dev, is given by dev = 2( lmax − l),where lmax is logarithm of the likelihood function of the full model and l is logarithm of the likelihood function of the proposed submodel. The deviances of the models are used for their comparison as described in the next theorem.Theorem 8. Consider GLM with vector of parameters βm and its submodel GLMsub with βq, where q < m < n. If the submodel GLMsub is suitable, then the diﬀ erence of deviances Δdev = devsub − devfulﬁ lls asymptotically χ2 distribution with (m − q ) degrees of freedom. For more details see Kaas (2009). Hence, for Δdev > χ21−(m − q ) we reject the assumption that the submodel is suitable.2.2.2 Information CriteriaThere are no perfect models. The idea is to ﬁ nd a model which is the best approximation of reality . We try to minimize the loss of information. The information criteria indicate that information is lost, when a model is used to describe the reality . They balance between accuracy of ﬁ tting the data and complexity of the model. Information criteria for selecting the minimal „good“ model are for example: • Akaike information criterion (AIC), • Schwarz-Bayesian information criterion (BIC), • Hannan-Quinn information criterion, • Deviance information criterion (DIC). In our case study , Akaike information criterion will be used for comparison of the models. I: Commonly used link functions Distribution Link function g(μ) normal identity μpoisson log ln(μ)binomial logit ln1 cloglog ln ln 1n exponential log ln(μ) 386 Silvie Kafková, Lenka KřivánkováDeﬁ nition 9. Akaike information criterion (AIC) is given as AIC = −2 l + 2 k,where k is the number of model parameters and l is logarithm of the likelihood function of the proposed model. Preferred model is considered to be that with the lowest AIC.3 RESULTS AND DISCUSION Every person, when applying for vehicle insurance policy , is assigned to a class, that is homogeneous in terms of risk. One of the criteria used for assigning an individual to a certain class is the number of claims. Thus, it is very important task for insurance companies to model the number of claims in a given insurance portfolio.Our aim is to predict relation of annual claim frequency on given risk factors. A data set from vehicle insurance will be processed. The data for our case study can be found in (Heller and Jong, 2008). The data set is based on one-year
claim frequency on given risk factors. A data set from vehicle insurance will be processed. The data for our case study can be found in (Heller and Jong, 2008). The data set is based on one-year vehicle insurance policies recorded in 2004 or 2005. There are 57 410 policies and 3 913 of them (6.82%) have at least one claim. The total amount of claims is 4 176. We see, that the histogram of annual claim frequency is strongly right-skew (Fig. 1).The GLMs are suitable for analysis of non-normal data, i.e. insurance data. Necessary procedures 02040608010012014016000.040.080.120.160.20.240.280.320.360.40.440.480.520.560.60.640.680.720.760.80.840.880.920.9611.4Frequency ofACFAnnualClaimFrequency (ACF)1: Histogram of Annual Claim Frequency II: V ariables in a data setNotation Name of Variable Range expo Exposure 0–1clm Claim occurrence 0 (no), 1 (yes)numclaims Number of claims 0, 1, 2, … veh_body Vehicle body type hatchback, sedan, station wagonveh_age Vehicle age 1 (new), 2, 3, 4 area Area of residence A, B, C, D, E, Fgender Gender male, femaleagecat Age band of policyholder 1 (youngest), 2, 3, 4, 5, 6 Generalized Linear Models in Vehicle Insurance 387are implemented in R soexpo).We try to ﬁ nd well-ﬁ tting GLM for the claim frequency in terms of the risk factors. For the number of claims per contract, it is reasonable to assume Poisson distribution. Our ﬁ rst GLM for data ﬁ tting is a model from Poisson family with log-link, which parameters are predicted in T ab. III. The coeﬃ cients are given relatively with respect to the standard class (veh_body1, veh_age1, area1, gender1, agecat1). The coeﬃ cients are taken to be zero for the standard class.According to predicted parameters, the best group is the one with veh_body1, veh_age4, area4, gender2 and agecat6. The corresponding average number of claims equals to e(−1.62140−0.12863−0.11371−0.01132−0.45845) = 0.097.That means one claim per 10.3 years on average. 3.1 Comparison of the Models In this subsection, the models with diﬀ erent risk factors are compared. In the following T ab. IV we test the null hypothesis that adding a risk factor to our preceding model actually has no eﬀ ect. The deviance (dev) for assessing the suitability of the proposed submodel is used. We assume the diﬀ erence in deviance (Δdev) between the preceding model and the proposed model has χ2 distribution with Δdf degrees of freedom. This is given in Theorem 8, where preceding model is a submodel of the proposed model.According to the analysis of deviance, the best model is 1+agecat+veh_age. However, we choose the model 1+agecat+veh_age+area, although Δdev = 10.58 < χ20.95(5) = 11.07. The test of the statistic is close to the critical value of χ2 distribution. We can support the inclusion of the parameter area by calculation of AIC.Although the AIC penalizes the number of parameters, the selected model has smaller AIC than its submodel, for the model 1+agecat+veh_age it is AIC = 127 900 and for the model 1+agecat+veh_age+area it
the AIC penalizes the number of parameters, the selected model has smaller AIC than its submodel, for the model 1+agecat+veh_age it is AIC = 127 900 and for the model 1+agecat+veh_age+area it holds AIC = 127 200. Hence, according to AIC, the model is improved. Furthermore, based on an educated guess, signiﬁ cance of the factor area is not negligible.4 CONCLUSIONConsidering that real data from vehicle insurance is not normally distributed, we cannot use the standard linear regression model. This paper proposes an estimate of annual claim frequency in vehicle insurance based on General Linear Model. It represents a work devoted to better understanding, using data of vehicle insurance, and how GLMs can be used to explain the relation of annual claim frequency on given risk factors.The case study results conﬁ rm the importance of three factors: age group of policy holder (agecat), vehicle age (veh_age) and area of residence (area). This particular case study shows that the gender III: The estimate of parameters Coeﬃ cients(Intercept) veh_body2 veh_body3 veh_age2 veh_age3 veh_age4 −1.62140 0.06056 0.09926 0.05294 −0.07510 −0.12863 area2 area3 area4 area5 area6 gender2 0.04384 0.01784 −0.11371 −0.01835 0.11873 −0.01132agecat2 agecat3 agecat4 agecat5 agecat6 −0.16865 −0.23317 −0.23977 −0.45026 −0.45845IV: The table of analysis of deviance Model speciﬁ cation df dev Δdev Δdf 1 855 1048.0 1+veh_body 853 1043.3 4.71 21+veh_age 852 1027.0 20.99 31+area 850 1033.2 14.82 51+gender 854 1047.7 0.38 11+agecat 850 972.7 75.33 51+agecat+ veh_age 847 953.5 19.16 31+agecat+veh_age+ area 842 942.9 10.58 5 388 Silvie Kafková, Lenka Křivánkováor vehicle body type (veh_body) are relatively unimportant for annual claim frequency .When the model was being created, we also had in mind the principle of simplicity . Therefore, we used analysis of deviance to compare relevance of the submodels. Our proposed model is quite simple, which is important for its use in practice.SUMMARYThe aim of this paper is to estimate an annual frequency of claims (AFC) from which the premium in vehicle insurance is derived. It is considered that the AFC depends on many risk factors. We take into account these ﬁ ve factors – vehicle body type, vehicle age, area of residence, gender of policyholder and age band of policyholder. The generalized linear models (GLMs) are used for the estimation of AFC in this paper. This approach is compared with commonly used linear regression and the advantages of GLMs are shown. In the initial section, the framework of GLMs is introduced, including the deﬁ nition of the link function and the speciﬁ cation of the exponential family of probability density functions. Then methods of model comparison, analysis of deviance and minimization of the information loss, are shown. The main part of the paper consists of a case study , where the GLMs are applied in vehicle insurance. We process a data set based on 57 410 one-year vehicle insurance policies. The drivers are
The main part of the paper consists of a case study , where the GLMs are applied in vehicle insurance. We process a data set based on 57 410 one-year vehicle insurance policies. The drivers are divided into groups on the basis of the risk factors. For each group, we model the average number of claims per contract. The aim is to ﬁ nd a well-ﬁ tting GLM for the claim frequency in terms of the risk factors. The Poisson distribution is assumed for the number of claims per contract and the log-link function is used. Several diﬀ erent models containing various risk factors are considered. Analysis of deviance, based on a comparison of the goodness of ﬁ t, is used to select the best model. According to the analysis of deviance, the suitable model has two risk factors (age group of policyholder and vehicle age). Nevertheless, the more complex model with one other factor (area of residence) is taken into account. The signiﬁ cance of the factor area is not negligible in practice. Although the signiﬁ cance of the risk factor area is rejected at a signiﬁ cance level of 0.05, it is not rejected at a signiﬁ cance level of 0.1. The choice of the model with the factor area is substantiated by the calculation of Akaike information criterion (AIC), which is based on minimizing the information loss. The approach introduced in this paper proves to be a useful way to implement methodics of the generalized linear models into actuarial science.REFERENCES ANTONIO, K., BEIRLANT, J., 2007: Actuarial statistics with generalized linear mixed models. Insurance: Mathematics and Economics, 40, 1: 58–76. ISSN 0167-6687.CERCHIARA, R., EDWARDS, M., GAMBINI A., 2008: Generalized linear models in life insurance: decrements and risk factor analysis under Solvency II. In: 18th International AFIR Colloquium. Available online: cfm?lang=EN&DSP=AFIR&ACT=COLLOQUIA.DENUIT, M. et al., 2007: Actuarial modelling of claim counts: risk classiﬁ cation, credibility and bonus-malus systems. Hoboken: Wiley , 384 p. ISBN 978-0-470-02677-9. DOBSON, A. J., 2002: An Introduction to Generalized Linear Models. Boca Raton: CRC Press, 225 p. ISBN 1-58488- 165-8.GSCHLÖSSL, S., SCHOENMAEKERS, P ., DENUIT, M., 2011: Risk classiﬁ cation in life insurance: methodology and case study . European Actuarial Journal, 1, 1: 23–41. ISSN 2190-9733.HABERMAN, S., RENSHAW , A. E., 1996: Generalized linear models and actuarial science. The Statistician, 45, 4: 407–436. ISSN 0039-0526.HARDIN, J. W ., HILBE, J., 2007: Generalized linear models and extensions. T exas: Stata Press, 387 p. ISBN 1597180149. HELLER, G. Z., JONG P ., 2008: Generalized Linear Models for Insurance Data. New Y ork: Cambridge University Press, 204 p. ISBN 0521879140.KAAS, R. 2009: Modern Actuarial Risk Theory: Using R. Heidelberg: Springer, 400 p. ISBN 9783642034077.MCCULLAGH, P ., NELDER, J. A., 1989: Generalized Linear Models. London: Chapman and Hall, 532 p. ISBN 0412317605. NELDER, J. A., WEDDERBURN, R. W . M., 1972: Generalized linear models.
9783642034077.MCCULLAGH, P ., NELDER, J. A., 1989: Generalized Linear Models. London: Chapman and Hall, 532 p. ISBN 0412317605. NELDER, J. A., WEDDERBURN, R. W . M., 1972: Generalized linear models. Journal of the Royal Statistical Society: Series A (General), 135, 3: 370–384. ISSN 0035-9238.OHLSSON, E. JOHANSSON, B., 2010: Non-life insurance pricing with generalized linear models. Berlin / Heidelberg: Springer, 174 p. ISBN 978-3-642-10790-0.WOLNY -DOMINIAK, A., 2012: Modeling of claim counts using data mining procedures in R CRAN. In: RAMÍK, J. and STAVÁREK, D. (eds.) Proceedings of 30th International Conference Mathematical Methods in Economics. Karviná: Silesian University , School of Business Administration, 980–985. ISBN 978-80- 7248- 779-0.Contact informationSilvie Kafková: 175424@mail.muni.czLenka Křivánková: 142474@mail.muni.cz
Int. J. Advance Soft Compu. Appl, Vol. 8, No. 3, December 2016 ISSN 2074 -8523 Predictive Modelling for Motor Insurance Claims Using Artificial Neural Networks Zuriahati Mohd Yunos1, Aida Ali2, Siti Mariyam Shamsyuddin2, Noriszura Ismail3, Roselina Sall eh@Sallehuddin1 1Faculty of Computing Universiti Teknologi Malaysia , Johor, Malaysia 2UTM Big Data Centre, Universiti Teknologi Malaysia , Johor Malaysia 3Pusat Pengajian Sains Matematik, Universiti Kebangsaan Malaysia , Selangor, Malaysia e-mail: zuriaha ti@utm.my, mariyam@utm.my, aida@utm.my , roselina@utm.my , ni@ukm.my Abstract The expected claim frequency and the expected claim severity are used in predictive modelling for motor insurance claims. There are two categor y of claims were considered, namely, third party property damage (TPPD) and own damage (OD) . Data sets from the year 2001 to 2003 are used to develop the predictive model. The main issues in modelling the motor insurance claims are related to the nature of insurance data, such as huge information, uncertainty, imprecise and incomplete information; and classical statistical techniques which cannot handle the extreme value in the insurance data. This paper proposes the back propagation neural network (BPNN) model as a tool to model the pro blem. A detailed explanation of how the BPNN model solves the issues is provided. Keywords : predictive modelling, c laim frequency, claim severity, back propagation neural network . 1 Introduction Predictive modelling is a process that involves problem identification, analysis of data, model development, prediction and validat ion . Predictive modelling in the insurance industry helps actuaries and other insurance analysis employing predictive models to enhance business operations that were previousl y using human expertise. Historically, actuaries performed their duties using pencil and paper before the advent of computers. Today, more advanced computing tools are Z. M. Yunos et al. 161 available . Predictive modelling has provided a set of instruments to the insurance companies for a variety of intentions from pricing to underwriting and claim handling . Moreover, the influences of predictive modelling are also dependent on the quality of the data used to generate the model. Insurance is a unique type of agreement between the insurer or insurance company and the insured or client in which the insurers permit that upon the occurrence of specific events, whether to make a payment to clients or cover the specific costs. There are two types of insurance that are life insu rance and general insurance, and motor insurance is under general insurance. This research focuses to develop a predictive model for motor insurance claim by estimating the two important components, namely, claim frequency and claim severity , , , , , . Claim frequency is defined as the number of claims per exposure unit, whereas claim severity is defined as the average claim cost per claim . The modelling of claim frequency
severity , , , , , . Claim frequency is defined as the number of claims per exposure unit, whereas claim severity is defined as the average claim cost per claim . The modelling of claim frequency and claim severity needed an information of exposure, n umber of claims and the amount of the claim (cost). The expected of claim frequency and claim severity can be calculated through a process of identifying grouping risk, which having the same characteristics is also known as risk classification. Thus, this study investigates how capable artificial neural networks (ANN) is as a potential technique to be applied in modelling the motor insurance claims problem. The utility of ANNs has been demonstrated in the insurance industry such as , and also was fo und in , , , , . In this paper, we intend to highlight the importance of the ANN approach in modelling claim frequency and claim severity. The remainder of this paper is organized as follows: Section 2 presents related works. Section 3 discuss es the BPNN model development is described. In Section 4 presents the experimental results and analysis . Finally, the conclusion is provided in Section 5. 2 Related Works Two important issues that were highlighted in motor insurance claims are the data and techniques, and these issues are interrelated among others . The first issue is related to the characteristics of insurance data which contain huge information or large number of variables, uncertainty, information is very noisy and incomplete information and this was agreed by , , , , . Hence, t he development of the predictive model in motor insurance claims requires sufficient data to acquire an accurate model. Besides that, t he predictive models are used for risk classific ation and to determine the premium , . The development of predictive models in motor insurance claims is known as risk classification. Risk classification is defined as the formulation of different premiums for the same coverage based on group chara cteristics. The group characteristic refer to the data or variables and is called rating variables or rating factors. The problem is how to determine and choose the significant rating factors and rating classes in risk classification , and this is related to the data issue and the techniques. It has been acknowledged by , . Another study also found a premium can be determined by a number of factors such as the vehicle cubic capacity, the 162 Predictive Modelling for Motor Insurance geographic zone where the insured lives, the aged of the insured , , , , . Extreme values or outliers can attract the insurers because it can help the insurers to determine the amount of the highest demands and protect themselves in the future. The second issue is related to the complexity of statistical analysis that has become more apparent. Due to this, actuaries had to solve the problem of finding a model that can explain re alistically the event of risk , and a model that able to handle complex problems in
has become more apparent. Due to this, actuaries had to solve the problem of finding a model that can explain re alistically the event of risk , and a model that able to handle complex problems in exploiting varying information . The suggestion of ANN approach to motor insurance claim is the use of past experience to train the network to provide more cons istent and reliable evaluations on claim frequency and claim severity. ANN, have been massive and it can process a large volume of uncertainty, inaccurate and lacking data, and also to look for estimate , , , , . Furthermore, ANN has been applied in the ﬁelds of ﬁ nance and economics , and many businesses use the ANN in their decision support systems. The input of training data and output for claim frequency and claim severity is shown in Table 1.1 and 1.2. For claim frequency, each data is used to determine the number of claims made by the insured (clients) and as claim severity the data are used to compute the amount claimed by the insured or amount paid by the insurer to insured. Following are the abilities of using ANN which can improve the predic tion with promising results. i. ANN is capable to handle a nonlinear and easily learn rich representations through the mapping of inputs to outputs. ii. ANN are flexible in how they can be use d such as pattern recognition, time series, and image processing and so on. iii. ANN is more successful in terms of speed, simplicity and capacity compared to traditional statistical models. iv. The performance of the ANN can be improved by tuning the parameters through trial -and-error . v. MATLAB provides ANN toolbox which can easily be used for training and testing. The implementation will be discussed in the next section. Z. M. Yunos et al. 163 Table 1.1: Input and output variables for TPPD, TPBI and Theft claim Notation Claim Frequency Claim Severity Input nodes Output nodes Input nodes Output nodes F1 Coverage Claim frequency Coverage Claim severity F2 Vehicle made Vehicle made F3 Vehicle cc Vehicle cc F4 Vehicle year Vehicle year F5 Location Location F6 Exposure - F7 - Number of claim Table 1.2 : Input and output variables for OD cla im Notation Claim Frequency Claim Severity Input nodes Output nodes Input nodes Output nodes F1 Coverage Coverage F2 Vehicle made Claim frequency Vehicle made Claim severity F3 Vehicle cc Vehicle cc F4 Vehicle year Vehicle year F5 Location Location F6 Exposure - F7 - Number of claim 3 Model Development Using ANN BPNN is one of the algorithm in ANN with a three -layer network structure of a back propagation (BP) learning algorithm is choose to model the motor insurance claims. There are two main steps involved; the ANN architecture and the BP algorithm. The essential steps for designing BPNN model are summarized in Table 1.3. In particular, step 1 to step 4 are carried out on data pre -processing, where the raw data is scaled and norm alized to an appropriate format to facilitate the predicting process. Step 5, which is
In particular, step 1 to step 4 are carried out on data pre -processing, where the raw data is scaled and norm alized to an appropriate format to facilitate the predicting process. Step 5, which is the step that designs the ANN model, involves the determination of the following variables: i. number of input nodes ii. number of hidden layers and hidden nodes iii. number of outp ut nodes iv. activation function 164 Predictive Modelling for Motor Insurance Table 1.3: Steps in designing a BPNN model Step 1 Variable selection Step 2 Data collection Step 3 Data normalization Step 4 Data division: training and testing Step 5 Determine the : - number o f input nodes - number of hidde n layers - number of hidden nodes - number of output nodes - activation function Step 6 ANN training by applying BP algorithm : - set the learning rate and momentum - set the number of training iterations Step 7 Model evaluation In Step 2, data normalization is implemented to smooth out the data, resulting in better data generalization and improved performance . The normalization function is based on the maximum and minimum values that could be set and is suggested by . The normalization formula used is given in Equation (1) : minmax min minmax min-( - )-tnewX XX D D DX X  (1) where Xt is the value will be normalized, minX is the minimum value of the statistic variable, andmaxX is the maximum value of the statisti c variable. maxD and minD are the maximum and the minimum values needed for normalization. The values of maxD and are set to 0.95 and 0.0, respectively and thes e values are used in this study. The normalization equation is selected due to the range of the activation function are between 0 to 1, and utilized in the BPNN. Hence , the outputs of a set date should be scaled to within this range. Another important step is data division. The data is broken down into two parts, training set and testing set. The training set is used for model development, and testing set is used to prediction . Basically, there is no guideline to divide the data. However, suggested tha t the data need to be divided by a ratio written in percentages, such as 90%:10%, 80%:20% and 70%:30%, with a total of 100% for the combined ratio. The percentage ratio of 70%: 30% is used and utilized in a cross validation technique to build an appropriat e model and to avoid over -fitting , . Table 1 .4 shows the data division with a ratio of 70%:30% for each category of claims . A single hidden layer is used and the determination of the number of hidden nodes is done via a trial -and-error method . The related ill ustration is given in Fig. Z. M. Yunos et al. 165 1.1. Basically, the purpose of a hidden layer is to detect the features, to capture the data pattern, and to perform the complicated non -linear mapping between the input and the output variable s. Hence, we applie d suggestion to determine the number of hidden nodes, whether they are “ n", or “ 2n", or “ 2n+1 ”, where “ n” is the number of
mapping between the input and the output variable s. Hence, we applie d suggestion to determine the number of hidden nodes, whether they are “ n", or “ 2n", or “ 2n+1 ”, where “ n” is the number of input nodes. The number of input nodes is predetermined by trial and error in the proposal stage based on the data given by Insu rance Services Malaysia Berhad (ISM). Another factor to be considered is the learning rate ( ) and the momentum ( ) where the value is in the range of 0 to 1. By using different values of learning rate and momentum, the learning proces s can be speeded up, causing the network convergence to be either slower or faster. However, the choice of learning rate and momentum can be very sensitive . Hence, a simple way to choose the learning rate and the momentum is through a trial and error -method. The BP algorithm involves two phases, the forward phase and the backward phase. In the forward phase, the activations are propagated from the input to the output layer, while in the backward phase, if the output pattern is different from the desir ed output, the error between actual and predicted values in the output layer is calculated and propagated backwards to modify the weights and bias values. The most popular error function used for the output layer is the mean sum squared error. The activat ion function ensures the relationship between the input and the output of a node. The network is trained with a pre -defined stopping criterion; either the number of iterations has been reached or when the total sum of square errors is lowers than a pre-determined value. This is the core part of ANN. The summary of the BPNN architecture and parameters used are shown in Table 1.5 and Table 1. 6 describes the tested network structures . By applying the parameters show in Tabl e 1.5 and depends on the process of trial and error with some considerations to give the best predictive result. Fig. 1.2 illustrates the network structure model with different number of hidden layer based on Table 1.6. Table 1.4: Data division with 70%:30% Category of claims Actual TPPD Training 741 Testing 318 Total data 1059 OD Training 386 Testing 166 Total data 552 166 Predictive Modelling for Motor Insurance Fig. 1.1: BPNN proposed model for motor insurance claim Table 1. 5: Summary of standard BPNN architecture and parameters Number of input nodes 4,5 and 6 Number of hidden layer 1 Number of hidden nodes See Table 1.4 (tested network structures) Number of output nodes 1 Learning rate 0.3 Momentum 0.9 Activation function Input to hidden layer sigmoid Hidden layer to output sigmoid Error per formance Mean square of error (MSE) Table 1. 6: Tested network structures 4-4-1 4-8-1 4-9-1 5-5-1 5-10-1 5-11-1 6-6-1 6-10-1 6-12-1 Adjust ANN parameters Predicted output inputs BPNN compare Actual output Z. M. Yunos et al. 167 Fig. 1.2: Network structure model with different number of hidden layer 6-6-1 network 6-12-1 network 6-13-1 network 5-5-1 network 5-10-1 network 5-11-1
compare Actual output Z. M. Yunos et al. 167 Fig. 1.2: Network structure model with different number of hidden layer 6-6-1 network 6-12-1 network 6-13-1 network 5-5-1 network 5-10-1 network 5-11-1 network 4-4-1 network 4-8-1 network 4-9-1 network 168 Predictive Modelling for Motor Insurance The fin al step is model evaluation and validation. Four statistical methods were used to measure the constructed models such as mean squared of error ( MSE), root mean square of error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) . The MAPE measures the absolute error as a percentage. A lower percent or closer to zero deviation implies a more accurate prediction. The best model is chosen based on four error measurements, RMSE, MSE, MAPE, and MAE. If the results given by the four error measurements are inconsistent, then MAPE is chosen as a benchmark. These statistical methods were chosen because of the wide applicability , , , , . 4 Experimental Results and Analysis This study discusses the two models namely, claim freq uency and claim severity and were tested on two category of claims which are TPPD and OD. The development of BPNN model is done through trial -and-error with the aim to obtain the best predictive result for claim frequency and claim severity . Thus, nine networks have been developed (see Table 1.4) and tested on the two models. Thus, from the nine network structures, the best model is chosen based on the smallest error value o f the MSE, RMSE, MAE and MAPE. The results of the best BPNN model for claim frequen cy and claim severity for each category of claims are outlined in Table 1.7 and Table 1.8, respectively. The experimental result reveals that the number of input nodes and hidden nodes, as well as the parameters chosen influence t he predictive accuracy. As a result , the best networks for each category of claims are shown in Fig. 1.3 and 1.4. The criterion used to determine the best BPNN model by looking at the lowest error value given by MSE, RMSE, MAE and MAPE. However, if the result produced by the four error measurement is inconsistent, then MAPE is chosen. As a conclusion, the BPNN is capable of producing a reliable prediction for motor insurance claims. Table 1.7: Best BPNN model for claim frequency Category of claims Network Claim frequency MSE RMSE MAE MAPE TPPD 6-13-1 369.50 19.22 10.73 0.2191 OD 4-9-1 3383.56 58.17 32.49 0.2169 Note : Best parameters chosen through trial -and error with learning rate = 0.3, momentum = 0.7 Table 1.8: Best BPNN model for claim severity Category of claims Netwo rk Claim severity MSE RMSE MAE MAPE TPPD 6-12-1 2870793.89 1694.34 1105.20 0.6515 OD 4-8-1 8441272.93 2905.39 2097.01 0.3261 Note: Best parameters chosen through trial -and error with learning rate = 0.3, momentum = 0.7 Z. M. Yunos et al. 169 0500100015002000250030003500TPPDOD MSE 0102030405060TPPDOD RMSE 05101520253035TPPDOD MAE 00.050.10.150.20.25TPPDOS MAPE Fig. 1.3: Comparison based on error measurements
= 0.7 Z. M. Yunos et al. 169 0500100015002000250030003500TPPDOD MSE 0102030405060TPPDOD RMSE 05101520253035TPPDOD MAE 00.050.10.150.20.25TPPDOS MAPE Fig. 1.3: Comparison based on error measurements for claim frequency 010000002000000300000040000005000000600000070000008000000 TPPDOD MSE 050010001500200025003000TPPDOD RMSE 03006009001200150018002100TPPDOD MAE 00.10.20.30.40.50.60.7TPPDOD MAPE Fig. 1.4: Comparison based on error measurements for claim severity Fig. 1.3 and 1.4 show that among the four error measurements , MAPE error is the easier to understand and represent a smallest value of error for claim frequency and claim severity. 5 Conclusion In this paper, we use BPNN as a learning tool for motor insurance claim in predictive modelling. The model development using this has been discuss ed in details. It is concluded that the BPNN model is successful in predictive modeling the Malaysian motor insurance claims by using several of network structures. Several factors that significantly influenced the performance of the BPNN have also been d iscussed, namely the network structure (number of input nodes and number of hidden nodes), data preprocessing, the parameters and the error measurement. The main advantage of using BPNN is that the model is capable of dealing with non -linear data. ACKNO WLEDGEMENT S This research is supported by the Ministry of Higher Education of Malaysia under a grant number (R.J130000.7828.4F606). The authors would like to thank the Ministry of Higher Education of Malaysia (MOHE), UTM Big Data Centre 170 Predictive Modelling for Motor Insurance (UTM -BDC) of Ibnu S ina Institute for Scientific and Industrial Research (ISI -SIR), Universiti Teknologi Malaysia for their support in this study. References Aftab, S., Abbas, W., Bilal, M.M., Hussain, T., Shoaib, M. and Mehmood, S.H. 2013. Data mining in insurance claim s (DMICS) two -way mining for extreme values, International Conference on Digital Information Management (ICDIM), pp. 1-6, 10 -12. Azlan, M. Z., Habibollah, H. and Safian, S. 2010. Prediction of surface roughness in the end milling machining using Artifi cial Neural Network, Expert Systems with Applications , 37(2):1755 -1768. Bahia, H. S. I. 2013. Using Artificial Neural Network Modelling in Forecasting Revenue: Case Study in National Insurance Company/Iraq, International Journal of Intelligence Science , 3(3):136 -143. Baser, F. and Apaydin, A. 2010. Calculating Insurance Claim Reserves with Hybrid Fuzzy Least Squares Regression Analysis. Gazi University Journal of Science , 23(2):163 -170. Batty, M., Tripathi, A., Kroll, A., Peter Wu, C -S., Moore, D., Stehno, C., Lau, L., Guszcza, J. and Katcher, M. 2010. Predictive Modelling for Life Insurance, Deloitte Consulting LLP (April). Christmann, A. (2004). An approach to model complex high -dimensional insurance data , Allgemeines Statistisches Archiv , 88: 375 -397. Chu, F. L. 2009. Forecasting tourism demand with ARMA -based methods, Tourism Management ,
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Classifying Risks On Motor Insurance Policies For I FRS 17 Implementation In General Insurance Companies Andiansyah Prima Wardana1, and Danang Teguh Qoyyimi2* 1Actuarial Unit, PT Asuransi Jasaraharja Putera, Jakarta, Indonesia 2Departement of Mathematics, Universitas Gadjah Mada, Yogyakarta, DI Yogyakarta, Indonesi a Abstract. IFRS 17 is a financial accounting standard issued by the International Financial Reporting System that regulates internationally agreed accounting treatment for insurance contracts. In an effort to increase the accuracy of risk assessment for IFRS 17 adaptation, a good way is needed to classify risks from the insured. Therefore, it is necessary to determine the risk group. Because data fro m an insurance company is large, the CLARA method is suitable for dealing with the problem. CLARA has a more robust nature of outliers and can be used to handle large amounts of data. After grouping, it is important to know what factors cause a person to enter a certain group. For this, classification analysis is needed. Some classification analysis methods are XGBoost, SVM, and AdaBoost. Extreme Gradient Boosting and Adaptive Boosting is a technique in machine learning for binary or multiclass regression a nd classification problems that results in predictive models in the form of weak predictive models. Support Vector Machine (SVM) is a technique for making predictions, both in the case of regression and binary or multiclass classification. SVM has the basi c principle of linear classifier . 1. Introduction In 202 5, the insurance company's financial statement recording system will change from IFRS 4 to IFRS 17. Changes in the recording system from IFRS 4 to IFRS 17 require some adaptations between IFRS 4 and IFRS 17 itself to have several variations. The difference between IFRS 17 and the previous recording system lies in the recognition of earnings, financial statements and the calculation of liabilities. In calculating liabilities for IFRS 17, there are 3 models namely General Model, Variable Fee Model, and Premium Allocation Approach. All three models share the same principle, that is, a liability consists of three components: the present value of cash flows, risk margins (risk adjust ments), and unrecognized Contructual Service Margins (CSM). Risk margin is the adjustment of compensation to assume uncertain risks from non -financial risks. Unrecognized CSMs are deferred earnings which must be recognized for providing services *Corresponding author: qoyyimi@ugm.ac.id © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (htt ps:creativecommons.or gb y).ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 in the future. However, there are differences in the calculation of liabilities under the current conditions. The difference is that the current profit margin (CSM) component has not been amortized even though IFRS 17 requires
are differences in the calculation of liabilities under the current conditions. The difference is that the current profit margin (CSM) component has not been amortized even though IFRS 17 requires amortization of CSM for each risk group . Amortization of CSM requires a more accurate projection of future liabilities. The accuracy of the projection is determined by the accuracy of the risk assessment of the insured. In the way to improve the accuracy of the risk assessment, we need to classify the risks of the insured. In this case, the company needs to review the policies that are already in place and classify the risks properly. To determine the insurance risk groups, it can be seen from the amount of the insured's claim. Therefor e, the grou ping method is very necessary to determine how many groups and what methods cause the risk grouping to be optimal. There are many methods in statistics that aim to group data, one of them is CLARA (Clustering Large Applications) . Having known the existing risk groups, as an insurance company it is important to know what things are affecting the risk groups of the insured. For this reason, it is necessary to do a classification analysis to find out what variables affect the insured into the insurance risk group. There are several classification methods for handling large amounts of data that are commonly called machine learning. Some of them are Extreme Gradient Boosting, Support Vector Machine, and Adaptive Boosting. In this paper we will review all of these methods and see their relevance in classif ying risks on insurance products. For predictive purposes, the authors also analyse the variables that affect these risk groups. With this research, it is expected that in the long run insurance companies will be able to perform better risk projections, calculations, administration, and better CSM governance. For the long term, it is expected to increase the company's readiness for IFRS 17 implementation. 2. Clustering Large Application (CLARA) Clustering Large Application is the development of the PAM method, which was introduced by Kaufman and Rousseeuw in 1990. CLARA has a more robust nature of outliers and can be used to handle large amounts of data. In addition, CLARA is more efficient than PAM in computing time and storage problems for large data sets. CLARA uses a sampling approach, dividing data into several groups, after that applying the PAM algorithm to get the optimal medoid. The quality of the medoid produced is measured by the total difference (distance) between each object in the data set and the medoid in the sample. By taking a random sample, the medoid value from the s ample is expected to be close to the medoid value from the data set. The following algorithm grouping objects using the CLARA algorithm. Determine k as many clusters as you want to form. Many clusters are determined by researchers or based on statistical methods. Dividing data at random in several partitions with a fixed size.
Determine k as many clusters as you want to form. Many clusters are determined by researchers or based on statistical methods. Dividing data at random in several partitions with a fixed size. The sample size is minimal (40 + 2k). The number of partitions is determined first. Apply the PAM algorithm to each partition to get a medoid. Following are the steps of the PAM algorithm: a. Determine k as many clusters as you want to form. Many clusters are determined by researchers or based on statistical methods. b. Determine the initial medoid by randomly selecting k objects from the objects to be grouped. c. Calculate the distance of non -medoid objects to medoids in each cluster. d. Place the object based on the closest distance to the medoid then calculate the total distance obtained. e. Randomly select non -medoid objects in each cluster as new medoid candidates. 2ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 f. Calculate the distance of each non -medoid object with the new medoid candidate and place the object based on the closest distance to the new medoid candidate. After that, also calculate the total distance obtained with the new medoid candidate. g. Calculates the difference in total distance (S). S = total distance on new medoid candidates - total distance on old medoid. If the S value is less than zero, then the new medoid candidate becomes a new medoid or if the total distance of each object to the new medoid candidate is less than the total distance of each object to the old medoid, then the new medoid candidate becomes a new medoid. h. Repeat steps e until all three do not change medoid. Medoid does not change when a value of S> 0. In other words, when the total distance of each object is obtained with a new medoid candidate greater than the total distance of each object with the old med oid, there is no medoid exchange because the new medoid candidate is not more centralized than the medoid long. Therefore, the iteration process will stop. i. Calculates the distance between all objects in the data set that do not become medoid and objects that become medoid. j. The partition with the smallest amount of distance is selected. By using medoid which is the object that is located most centrally in a cluster, the k -medoids method is more robust than k -means. However, the k -medoids method with the CLARA algorithm is more effective for grouping large data compared to PAM. 3. Extreme Gradient Boosting (XGBoost) Gradient Tree Boosting or Gradient Boosted Regression Trees is a generalization of boosting to arbitrarily distinguish loss functions. Gradient Boosted Regression Trees are accurate and effective 'off -the-shelf' procedures for solving regression and classi fication problems. The Gradient Tree Boosting model is used in a variety of areas including web search and ecology ranking. Extreme Gradient Boosting was first introduced by Friedman. The advantage of the XGBoost algorithm is that it can use storage memory efficiently.
of areas including web search and ecology ranking. Extreme Gradient Boosting was first introduced by Friedman. The advantage of the XGBoost algorithm is that it can use storage memory efficiently. Extreme Gradient Boosting is a technique in machine learning for regression and classification problems that p roduces predictive models in the form of a weak predictive model and can be used in various types of data both numeric and categorical and can be used for various data formats namely text data, images, video and audio. The model development is done by usin g the boosting method, namely by creating a new model to predict the error / residual from the previous model. New models are added until there are no more corrections to errors that can be made. This algorithm is called gradient descent to minimize errors when creating new models. In the Extreme Gradient Boosting method, the data class used does not have to be balanced because this method can handle data that has an unbalanced class. However, the results will be much better if the data class used is balanc ed. In addition, unit sizes of class features need to be equalized because if units of size between features are not the same, the weights for features that have larger unit sizes will have greater weights. Fig. 1. Systematic Diagram of the XGBoost Algorithm 3ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 Figure 1 shows a schematic diagram of the XGBoost computation process with 𝑦̂𝑡(𝑡)=∑ 𝑓𝑘(𝑥𝑘)𝑡𝑘=1 and 𝑓𝑘(𝑥𝑘) illustrate the tree model and 𝑦̂𝑡𝑡 is obtained from the following calculation: 𝑦̂𝑡(0)=0 𝑦̂𝑡(1)=𝑓1(𝑥1)=𝑦̂𝑡(0)+𝑓1(𝑥1) 𝑦̂𝑡(2)=𝑓1(𝑥1)+𝑓2(𝑥2)=𝑦̂𝑡(1)+𝑓2(𝑥2) ⋮ 𝑦̂𝑡(𝑡)=𝑦̂𝑡(𝑡−1)+𝑓𝑡(𝑥𝑡) 𝑦̂𝑡(𝑡)=∑𝑓𝑘(𝑥𝑘)𝑡𝑘=1 (1) From equation 1, 𝑦̂𝑡(𝑡) is the final tree model, 𝑦̂𝑡(𝑡−1) is the previously generated tree model, 𝑓𝑡(𝑥𝑡) is the newly created model, and t is the total number of models from the base tree models. To find the optimal algorithm, it can be replaced by finding a new classifier that can reduce the loss function, with the target loss function displayed in the following equation: ℒ(𝜙)=∑ 𝑙(𝑦𝑖,𝑦̂𝑡𝑡)𝑡𝑖=1+∑ 𝛺(𝑓𝑖)𝑡𝑖=1 (2) Where 𝑦𝑖 is the actual value, 𝑦̂𝑡𝑡 is the predicted value, 𝑙(𝑦𝑖,𝑦̂𝑡𝑡) is the lost function, and Ω(𝑓𝑖)=𝛾𝑇+12𝜆‖𝑤‖2 is the regularization. The ensemble tree model in equation 2 includes functions as parameters and cannot be optimized using the optimization method in the Euclidean space so that the model is trained additively. Used 𝑦̂𝑡𝑡 in the i -th prediction and t -iteration, to minimize the loss function, we need to add 𝑓𝑖 to get the following equation: ℒ(𝑡)=∑ 𝑙(𝑦𝑖,𝑦̂𝑡𝑡−1)𝑡𝑖=1+𝑓𝑡(𝑥𝑖)+𝛺(𝑓𝑖) (3) To optimize objectives in general a second order approach is used and the following equation is obtained: Taylor series expansion function: 𝑓(𝑎+ℎ)=𝑓(𝑎)+𝑓′(𝑎)ℎ+12𝑓′′(𝑎)ℎ2+⋯+𝑓𝑛(𝑎)ℎ𝑛𝑛! with 𝑎=𝑦̂𝑡𝑡−1 ℎ=𝑓𝑡(𝑥𝑖) 𝑓(𝑎)=𝑙(𝑦𝑖,𝑦̂𝑡𝑡−1) Then Equation 3 becomes ℒ(𝑡)=∑ 𝑙(𝑦𝑖,𝑦̂𝑡𝑡−1)𝑛𝑖=1+(𝜕𝑙(𝑦𝑖,𝑦̂𝑡𝑡−1)𝜕(𝑦̂𝑡𝑡−1))𝑓𝑡(𝑥𝑖)+(𝜕2𝑙(𝑦𝑖,𝑦̂𝑡𝑡−1)𝜕(𝑦̂𝑡𝑡−1)2)𝑓𝑡(𝑥𝑖)2+⋯+𝛺(𝑓𝑡) (4) ℒ(𝑡)=∑ +𝛺(𝑓𝑡) (5) ℒ(𝑡)=∑ +𝛺(𝑓𝑡) (6)
𝑎=𝑦̂𝑡𝑡−1 ℎ=𝑓𝑡(𝑥𝑖) 𝑓(𝑎)=𝑙(𝑦𝑖,𝑦̂𝑡𝑡−1) Then Equation 3 becomes ℒ(𝑡)=∑ 𝑙(𝑦𝑖,𝑦̂𝑡𝑡−1)𝑛𝑖=1+(𝜕𝑙(𝑦𝑖,𝑦̂𝑡𝑡−1)𝜕(𝑦̂𝑡𝑡−1))𝑓𝑡(𝑥𝑖)+(𝜕2𝑙(𝑦𝑖,𝑦̂𝑡𝑡−1)𝜕(𝑦̂𝑡𝑡−1)2)𝑓𝑡(𝑥𝑖)2+⋯+𝛺(𝑓𝑡) (4) ℒ(𝑡)=∑ +𝛺(𝑓𝑡) (5) ℒ(𝑡)=∑ +𝛺(𝑓𝑡) (6) Suppose 𝑓𝑡 has as many leaf nodes as K, Ij is the jth node, and wj is a prediction for the nth node, then 𝛺(𝑓𝑡)=𝛾𝐾+12𝜆∑𝑤𝑗2𝐾𝑗=1 (7) 4ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 ℒ(𝑡)=∑𝐾𝑗=1+𝛾𝐾 (8) For each leaf j, 𝑑ℒ(𝑡)𝑑𝑤𝑗 𝑤𝑗∗=−(𝜆𝐼+𝐻̅𝑗)−1𝑔̅𝑗 (9) Assume that 𝑓𝑡 base learner improvements have K leaf nodes. For example, 𝐼𝑗 becomes the set belonging to node j and 𝑤𝑗 becomes the prediction for that node. Using the substitution of equation 9 to equation 8, the following equation is obtained: ℒ(𝑡)=−12∑(∑ 𝑔𝑖 𝑖∈𝑗)2∑ ℎ𝑖+𝜆 𝑖∈𝑗𝐾𝑗=1+𝛾𝐾 (10) The algorithm of the Extreme Gradient Boosting method is as follows: 1. Initialize the model with values: 𝐹0(𝑥)=𝑎𝑟𝑔𝑚𝑖𝑛 ∑ 𝑙(𝑦𝑖,𝑦̂𝑙)𝑛𝑖=𝐼 (11) or initialization using 0. 2. For the 1st iteration a. Calculate the value of the first derivative and the second derivative of the statistical gradient with the logistic loss function as follows : 𝑙(𝑦𝑖,𝑦̂𝑙)=𝑦𝑖𝑙𝑛(1+𝑒−𝑦̂𝑙)+(1−𝑦𝑖)𝑙𝑛(1+𝑒𝑦̂𝑙) (12) 𝑔𝑖(1)=−(𝑦𝑖−1)𝑒𝑦̂𝑖(0)+𝑦𝑖𝑒𝑦̂𝑖(0)+1 (13) ℎ𝑖(1)=𝑒𝑦̂𝑖(0)(𝑒𝑦̂𝑖(0)+1)2 (14) b. Determine the best separation, which will increase the prediction at most or reduce the value of the loss function at most. For example the separation for leaf = 2 with the first leaf 𝐼𝐿 and the second leaf 𝐼𝑅 using the ℒ𝑠𝑝𝑙𝑖𝑡 equation or called gain. c. Do point b to observe each leaf. The algorithm will calculate the gain scores for all split potentials on each leaf separately to see if there are new branches with positive gain that can be added to one of two leaves or both leaves. d. Calculate the weight value for each leaf. e. Carry out points a through d for the next iteration. 3. Combine the tree model obtained to predict new data. Add up all the weights of each tree and then transform it into probability. 4. Support Vector Machine (SVM) Support Vector Machine (SVM) is a technique for making predictions, both in the case of classification and regression . In the SVM method, the data class used must be balanced because if the data class is not balanced then this method cannot predict the minority class. In addition, unit sizes of class features need to be equalized because if the unit sizes between features are not the same, the weights for features that have larger unit sizes will have greater weights. This explanation has been explained in Chapter II. SVM has the basic principle of linear classifier, which is a case of classification that can be linearly separated, but SVM has been developed so that it can work on non -linear problems by incorporating the concept of the kernel in a high -dimensional workspace. In a high -dimensional space, hyperplane will be sought to maximize the distance between classes of data. 5ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 Initially, SVM was developed for the problem of class classification of two classes and then
maximize the distance between classes of data. 5ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 Initially, SVM was developed for the problem of class classification of two classes and then developed for multiclassical classification . In multiclass classification, hyperplane formed is more than one. One approach used is one on one (SLA). The SLA m ethod for the k-class classification case finds k hyperplane where k is a lot of classes and p is hyperplane. In this method, 𝜌(𝑡) is tested with all data from class l with label +1 and all data from other classes with label -1. The concept of SLA is, for example, in the case of three classes, classes 1, 2, and 3. If 𝜌(1) is to be tested, all data in class 1 is labelled by +1 and data from classes 2 and 3 are labelled by -1. In 𝜌(2), all data in class 2 are labeled +1 and data from class 1 and class 3 are labeled -1 as well as for 𝜌(3). After that, a hyperplane with two classes SVM algorithm will get a hyperplane for each of the above classes. After that, the class of a new data is determined based on the largest value of the hyperplane. 𝑐𝑙𝑎𝑠𝑠 𝑥=𝑎𝑟𝑔 𝑚𝑎𝑥ℓ=1,…,𝑘((𝑤(ℓ))𝑇.𝜙(𝑥)+𝑏(ℓ)) (15) 5. Adaptive Boosting (AdaBoost) AdaBoost is an acronym for Adaptive Boosting, this algorithm is widely applied to prediction models in data mining. The essence of the AdaBoost algorithm is to give more weight to inappropriate observations. AdaBoost is an ensemble learning that is often u sed on the boosting algorithm. AdaBoost itself is basically m linear combination of 𝑚𝑘𝑚(𝑥𝑖) classifier with classifier function, for example 𝑘𝑚(𝑥𝑖). Adaboost agar penulisannya konsisten and its variants have been successfully applied in several fields because of their strong theoretical base, accurate predictions, and great simplicity. The steps in the AdaBoost algorithm are as follows: 1. Initialize the weights of each observation with 𝑤𝑖=1𝑛 𝑢𝑛𝑡𝑢𝑘 𝑖=1,2,…,𝑛. 2. For m = 1 to m = M: a. Predict the class 𝑘𝑚(𝑥𝑖) for training data using 𝑤𝑖(𝑚) b. Calculate the error value with 𝑒𝑟𝑟(𝑚)=∑ 𝑤𝑖(𝑚) 𝑛𝑖=1 ; 𝑦𝑖 ≠𝑘𝑚(𝑥𝑖)∑ 𝑤𝑖(𝑚) 𝑛𝑖=1 c. Calculate the value 𝑎(𝑚)=𝑙𝑜𝑔1−𝑒𝑟𝑟(𝑚)𝑒𝑟𝑟(𝑚) d. Calculate 𝑤𝑖(𝑚)=𝑤𝑖(𝑚)exp(𝑎(𝑚))𝑤𝑖𝑡ℎ 𝑖=1,2,…,𝑛 𝑑𝑎𝑛 𝑦𝑖 ≠𝑘𝑚(𝑥𝑖) e. Normalize 𝑤𝑖(𝑚) 3. The output is the class of observation, 𝑐𝑙𝑎𝑠𝑠 𝑥=argmax𝑘(∑ 𝑎(𝑚) 𝑀𝑚=1 )𝑤𝑖𝑡ℎ 𝑘𝑚(𝑥𝑖)=𝑘. 6. Classification And Grouping Of Motor Vehicle Insurance Policies Before conducting data analysis, steps are taken to prepare data called preprocessing data. This step aims so that later the results of the analysis can be more accurate and on target and make the data size smaller without reducing information. The first step that the authors do for preprocessing data is to delete duplicate data. If there are two or more individuals with all the same variable values, only one sample will be written. If there is duplicate data, the analysis process is not optimal because the duplicate data is seen as two different data. This will certainly change the accuracy of the model for future analysis. There were 5
is duplicate data, the analysis process is not optimal because the duplicate data is seen as two different data. This will certainly change the accuracy of the model for future analysis. There were 5 data deleted to solve the problem of duplicate data in the data. The next step is 6ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 to delete the sample that has a total positive claim. Total claims can be obtained from the sum of gross claims, salvage, subrogation and adjustment. The total claim should be negative, the total positive claim is deleted because it is considered as an err or in recording data by company employees. There were 44 policies that were deleted because they had positive total claims. After that, the total claims are normalized with the insurance period so that the total size of the total claims becomes equal for e ach policy. The first step and the second step is done by the writer in the claim data. The third step is to combine claims data and premium data and then delete samples that are not claims because the authors only focus on samples that have received claims from the c ompany. Because the author only uses data for the transportation vehicle category, the total sample used for the study was 1,077 samples. Fig. 2. Boxplot data for total claims From the boxplot above, it can be seen that the total claim variable has many outliers so that to be able to form a cluster of the total claim variables cannot use the k -means cluster method because the k -means method is very sensitive to outliers. Therefo re, to form a cluster of total claim variables the CLARA (Clustering Large Applications) method is used. Like the k -means method, the CLARA method also groups samples into cluster k. Previously, the total claim variable had fulfilled the multicollinearity assumption because in the grouping of data only one variable was used. Before dividing the total claim data into cluster k , it is necessary to know the optimal k value from the possible k value. The author uses gap statistics to find out the optimal k value. Figure 3 shows some of the gap statistics shown in the plot. Fig. 3. Plot gap statistics for CLARA Figure 3 is a visualization of the gap -statistics values for the total normalized claims. It can be seen in Figure 4.3 that the highest gap statistics are at k = 5 and for k greater than 5 there is no statistical gap value greater than k = 5. Therefore, th e author decides to classify the total normalized claims into 5 clusters that refer to the gap -statistics of the total normalized claims. Grouping samples into five clusters using the CLARA method can be seen in the following table. 7ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 Table 1 . The results of grouping samples using the CLARA method Klaster Frekuensi Medoid (Rupiah) 1 607 -4.027.000 2 65 -457.917.808 3 255 -28.511.927 4 116 -169.654.795 5 34 -955.621.918 From table 1 it can be seen that the cluster 1 to cluster 5 has a medoid that has
Frekuensi Medoid (Rupiah) 1 607 -4.027.000 2 65 -457.917.808 3 255 -28.511.927 4 116 -169.654.795 5 34 -955.621.918 From table 1 it can be seen that the cluster 1 to cluster 5 has a medoid that has not sorted according to the cluster. The author does not sort the clusters of the smallest or largest medoids because sequencing does not change the results of further analys is. In addition, it appears that the most samples are in cluster 1, which is 607 samples with a medoid of -4,027,000. This shows that there are 607 samples with a total claim value of -4,027,000. There are 65 samples in cluster 2, 255 samples in cluster 3, 116 samples in cluster 4, and 34 samples in cluster 5 with different medoid values as shown in the table. The characteristics of each cluster sample can be seen in Figure 4. Fig. 4. Sample histogram for each cluster In Figure 4, histograms from cluster 1, 3, 4, and 5 have heavy tail properties, which are histograms that have mean < median < mode. Cluster 2 histograms tend to be like histograms whose skewness values are similar to normal distributions i .e. mode = median = mean values. This shows that cluster histograms 1, 3, 4, and 5 have many total claims that are greater than the average total claims whereas in cluster 2, the average total claims are almost the same as the mode . 8ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 After analysing the cluster, the writer found several characteristics of each variable for each cluster. Vehicles that get the most claims from companies are new vehicles, this is evident in each cluster mode for vehicle status is a new vehicle. The vehicle brands that g et the most claims are Mitsubishi and truck and box types. In cluster 1, the vehicles that get the most claims are vehicles that are often used for official purposes while in cluster 2, 3, 4, and 5 the vehicles that get the most claims are v ehicles that are often used for business purposes. In cluster 2, 3, 4, and 5 the location of the vehicle that received the most claims was in Sumatra while for cluster 1 it was in the Greater Jakarta area. After cluster analysis, the preprocessing stage needs to be carried out in preparation for the classification analysis. At this preprocessing stage, some handling is carried out, namely handling the imbalance data, transforming variables, making dummy var iables, and partitioning data. Data partition can be seen in the following table. Table 2. Data Partition Proporsi Traini ng Data Testing Data 0.6 0.4 0.7 0.3 0.8 0.2 The classification analysis is then performed using the XGBoost method. Classification analysis using Extreme Gradient Boosting Method is done by combining data partitions and parameters. The parameter to be combined is the eta parameter. The author uses three different eta parameters namely 0.01; 0.1; and 0.3. The author also uses a maximum of 1000 iterations (nrounds = 1000), the general parameter of the booster is gbtree, and the task parameter of the objective is
parameters namely 0.01; 0.1; and 0.3. The author also uses a maximum of 1000 iterations (nrounds = 1000), the general parameter of the booster is gbtree, and the task parameter of the objective is multi: softprob because it is used for classification with more than two classes. Table 3. Comparison of the accuracy value of the Extreme Gradient Boosting method Eta Parameter Training Data Testing Data Accuracy Training Data Accuracy Testing Data 0,01 0,6 0,4 0,8545 0,8699 0,7 0,3 0,8545 0,8804 0,8 0,2 0,8744 0,8896 0,1 0,6 0,4 0,8847 0,9028 0,7 0,3 0,8936 0,9155 0,8 0,2 0,9102 0,9325 0,3 0,6 0,4 0,8836 0,8962 0,7 0,3 0,8908 0,9122 0,8 0,2 0,9065 0,9308 Table 3 is the result of the analysis of the Extreme Gradient Boosting Method for multiclass cases. At the learning rate (eta) of 0.01, the highest accuracy value is at 80% of the training data partition and 20% of the testing data is 87.44% for the traini ng data and 88.96% for the testing data. At the learning rate (eta) of 0.1, the highest accuracy value is at 80% of the training data partition and 20% of the testing data is 91.02% for the training data and 93.25% for the testing data. At the learning rat e (eta) of 0.3, the highest accuracy value is at the 80% partition of training data and 20% of testing data that is 90.65% for training data and 93.08% for testing data. It can be seen that the highest accuracy value is 80% of training data partition and 2 0% of testing data and learning rate (eta) is 0.1 which is 91.02% for training data and 93.25% for testing data. In this case, it can be said that accuracy is higher 9ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 when the proportion of training data is higher and the best model when the eta parameter value is 0.1. Next we will see the goodness of the model for each class. Because previously the best accuracy value is a model with an eta parameter value of 0.1 and 80% partition training data and 20% testing data, it will be seen a measure of the goodness of the mode l for the best model that will be compared with the Support Vector Machine method. Table 4. Confusion matrix training data on the Extreme Gradient Boosting method From the table above it can be seen that the accuracy of the model for training data is 91.02%, which means the Extreme Gadient Boosting method can classify training data correctly (the accuracy of the method) by 91.02%. There is also a good measure of the model for each class. Class 1 sensitivity is 0.7122 which means that the ability of the model to predict class 1 data compared to actual class 1 data is 71.22%. Class 2 sensitivity is 1 which means that the ability of th e model to predict class 2 data compared to actual class 2 data is 100%. Class 3 sensitivity is 0.8560 which means that the ability of the model to predict class 3 data compared to actual class 3 data is 85.60%. Class 4 sensitivity is 0.9816 which means that the ability of the model to predict class 4 data compared to actual class 4 data is
to predict class 3 data compared to actual class 3 data is 85.60%. Class 4 sensitivity is 0.9816 which means that the ability of the model to predict class 4 data compared to actual class 4 data is 98.16%. Class 5 sensitivity is 1 which means that the ability of the model to predict class 5 data compared to actual class 5 data is 100%. It is also seen that the specificity of class 1 is 0.9779. This shows that the probability that the model predicts data other than class 1 compared to all predicted data is true in classes other than class 1 and the predicted data for class 1 but not class 1 is 97.79%. The specifi city value of class 2 is 0.9881 which means the chance of the model predicting data other than class 2 compared to all predicted data is true in classes other than class 2 and the predicted data for class 2 but not class 2 is 98.81%. The specificity value of class 3 is 0.9526 which means the chance of the model predicting data other than class 3 compared to all predicted data is true in classes other than class 3 and the predicted data for class 3 but not class 3 is 95.26%. The specificity value of class 4 is 0.9742 which means the chance of the model predicting data other than class 4 compared to all predicted data is true in classes other than class 4 and the predicted data for class 4 but not class 4 is 97.42%. The specificity value of class 5 is 0.9949 w hich means the probability of the model predicting data other than class 5 compared to all predicted data is true in classes other than class 5 and the predicted data for class 5 but not class 5 is 99.49%. In the same way the confusion matrix obtained from the testing data of the XGBoost, SVM, and AdaBoost methods as well as the confusion matrix training data for the SVM and AdaBoost methods. Prediksi ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 Table 5. Confusion matrix testing data on the Extreme Gradient Boosting method Table 6. Confusion matrix training data on the Support Vector Machine method Prediksi Table 7. Confusion matrix testing data on the Support Vector Machine method Prediksi Table 8. Confusion matrix training data on the Adaptive Boosting method Prediksi Table 9. Confusion matrix testing data on the Adaptive Boosting method Prediksi Prediksi ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 Because the analysis has been done using 3 methods, namely the SVM (Support Vector Machine) method, the XGBoost (Extreme Gradient Boosting) method, and the AdaBoost (Adaptive Boosting) method for multiclass data, in this case the three methods will be compared based on the measures of goodness contained in the table 4 to table 9. Table 10. Comparison of the goodness of the SVM, XGBoost and AdaBoost methods Jenis data Training (%) Testing (%) Metode SVM XGBOOST ADABOOST SVM XGBOOST ADABOOST Akurasi 68,45 91,02 95,88 65,20 93,25 89,57 Sensitivitas kelas 1 77,51 71,22 92,46 70,11 78,23 71,05 Sensitivitas kelas 2 61,29 100 98,92 58,82 100 100 Sensitivitas kelas 3
SVM XGBOOST ADABOOST Akurasi 68,45 91,02 95,88 65,20 93,25 89,57 Sensitivitas kelas 1 77,51 71,22 92,46 70,11 78,23 71,05 Sensitivitas kelas 2 61,29 100 98,92 58,82 100 100 Sensitivitas kelas 3 86,60 85,60 88,40 71,25 89,26 80,00 Sensitivitas kelas 4 84,46 98,16 99,47 75,44 99,15 97,06 Sensitivitas kelas 5 58,71 100 100 61,97 100 100 Spesifisitas kelas 1 93,18 97,79 97,27 90,77 97,93 95,70 Spesifisitas kelas 2 95,70 98,81 99,93 93,61 98,99 99,59 Spesifisitas kelas 3 86,25 95,26 98,08 85,80 96,50 93,89 Spesifisitas kelas 4 88,79 97,42 99,79 89,46 98,16 98,11 Spesifisitas kelas 5 99,27 99,49 99,80 99,34 1 99,72 From table 10, it can be seen that in this case the XGBoost method is slightly superior to the AdaBoost method and far superior to the SVM method. The XGBoost method has 10 measures of goodness with the highest value while the AdaBoost method has 9 measures of goodness with the highest value. In addition, in the AdaBoost method, the accuracy of testing data is always worse than the training data of 4.8% to 7.9%. Therefore, in this problem, the XGBoost method is superio r to the SVM method or the AdaBoost method. Next, we will see what variables influence the decisions of the XGBoost method. Fig. 5. The Feature Importance value of the XGBoost method 12ITM Web of Conferences 58, 04006 (2024)The 6th IICMA 2023 From Figure 5 it can be seen that the variable that most influences the amount of a person's claim is the "TSI" variable, which is the variable that explains the maximum value of the insurance company covering the insured's loss. Next there is the variable "time of accident" and followed by the variable "age of the vehicle". After that, the variable that affects the amount of the claim is determined if the duration of the "insurance period" and followed by the variable "vehicle location" located in Sumatra. Variables that are very influential in class determinati on are the variables included in cluster 1, namely the "TSI" variable, the "accident time" variable, the "vehicle age" variable, and the "insurance period" variable. 7. CONCLUSION Based on the results of the analysis that has been presented previously and other explanations, several conclusions can be drawn as follows: 1. CLARA (Clustering Large Application) method is a cluster analysis method with medoid as the center of the cluster. This method is more robust than the k -means cluster method when the available data contains outliers. Apart from that, this method can also handle large data. 2. In this data, using a vehicle insurance data obtained by many optimal clusters of 5 clusters. Determination of optimal cluster using the gap -statistics method. 3. In the data preprocessing stage for this case, the researcher uses Random Over Sampling (ROS) in handling data imbalance cases. 4. Extreme Gradient Boosting, Support Vector Machine, and Adaptive Boosting methods can classify vehicle insurance data well. 5. The parameter tuning process in the training data aims to get the right
Extreme Gradient Boosting, Support Vector Machine, and Adaptive Boosting methods can classify vehicle insurance data well. 5. The parameter tuning process in the training data aims to get the right parameters so that a more accurate model is obtained than when no parameter tuning is performed. When the training model data is accurate enough, it is expected that the data testing m odel does not have a level of accuracy that is far different from the training data. 6. Extreme Gradient Boosting is a method for dealing with regression and classification problems that produce models in a combined form (ensemble) with gradient descent and boosting techniques to minimize errors when creating new models. 7. Support Vector Machine is a technique for making predictions both in the case of regression and classification. In high -dimensional space, SVM will look for hyperplanes that can maximize the distance between data classes. 8. Adaptive Boosting is widely applied to prediction models in data mining. The essence of the AdaBoost algorithm is to give more weight to inappropriate observations. 9. In the Extreme Gradient Boosting method with 80% data partition for training data and 20% data for testing data with eta parameter of 0.1 and 1000 iterations obtained the best accuracy value is 91.02% for training data and 93.25% for testin
Journal of Scientific & Industrial Research Vol. 83, February 2024, pp. 183-190 DOI: 10.56042/jsir.v83i2.4302 Motor Insurance Policy Selection: A Joint Spherical Fuzzy Analytic Hierarchy Process (SF-AHP) and Combined Compromise Solution (CoCoSo) Approach Mangesh Joshi Shri Ramdeobaba College of Engineering and Ma nagement, Nagpur 440 013, Maharashtra, India Received 23 July 2023; revised 22 Se ptember 2023; accepted 10 January 2024 Motor insurance policies play a crucial role in protecting vehi cle owners against financial lo sses due to accidents, theft, or other unforeseen events. The selection of an appropriate motor insurance policy is a complex decision-making process that requires considering multiple criteria and their interrel ationships. The motivation behind this study is to offer an advanced decision-making framework that addresses the complexities of motor in surance policy selec tion, improves risk management, fosters innovation in decisi on-making methodologies, enhances custom er satisfaction, and increases the competitiveness of insurance providers. This research presents a joint approach, combining the SF-AHP (Spherical Fuzzy Analytic Hierarchy Process) and the CoCoSo (Combined Compro mise Solution) method, to facilitate the selection of the most suitable motor insurance policy. The weights of the fact ors are estimated by SF-AHP met hod with experts’ advice. The rankings of the alternatives ar e calculated using CoCoSo method. The sensitivity anal ysis is also carried out to check the stability of results over different Eigen values ( ). Premium amount is identified as the most influencing factor with factors weight as 0.178 and reputation of the insura nce company is identified as least domina ting out of other selected factors with factor weight as 0.10. The results ar e significantly stable over different  values ranging from zero to one. The research paper addresses a novel problem of motor in surance policy selection that has not been explored by any previous researchers in the existing literature. Keywords: Analytic hierarchy process, Fuzzy sets, Multi-criteria decision-making, Ranking, Spherical AHP Introduction The Motor insurance is a form of insurance designed to provide financial protection against loss or damage to a vehicle, as well as liability for injuries or property damage caused to third parties. It is a mandatory requirement in many countries and can provide peace of mind for drivers knowing that they are protected in the event of an accident. Numerous varieties of motor insurance coverage exist, each meticulously tailored to safeguard against distinct hazards.1 Liability coverage is designed to protect against claims made by third parties for injuries or property damage caused by the insured's vehicle. This coverage is mandatory in most jurisdictions and typically includes both bodily injury liability and property damage liability. Collision coverage is designed to provide protection against damage to the
is mandatory in most jurisdictions and typically includes both bodily injury liability and property damage liability. Collision coverage is designed to provide protection against damage to the insured's vehicle in the event of an accident. This coverage is optional but may be required if the vehicle is financed or leased. Personal injury protection, or PIP, is designed to provide coverage for medical expenses and lost wages fo r the insured and their passengers in the event of an accident, regardless of who is at fault. This coverage is mandatory in some jurisdictions. The cost of motor insurance premiums can be affected by several factors, including driving record, age, vehicle type, and location.2 Drivers with a history of accidents or traffic violations are typically considered to be higher risk and may be charged higher premiums. Younger drivers are generally considered to be higher risk and may also be charged higher premiums. Vehicles th at are more expensive to repair or replace, or that have a higher likelihood of being stolen, may also result in higher premiums. Additionally, drivers in areas with high rates of accidents or theft may be charged higher premiums. Having adequate motor insurance coverage is essential for protecting oneself financially in the event of an accident.3 Without insurance, the costs of repairing or replacing a vehicle, as well as liability for injuries or property damage caused to others, can be prohibitively expensive. In addition to financial protection, having motor insurance can also provide peace of mind and help to ensure that drivers are able ————— — Author for Correspondence E-mail: joshimp@rknec.edu J SCI IND RES VOL 83 FEBRUARY 2024 184 to meet their legal obligations. In many jurisdictions, driving without insurance is illegal and can result in fines, license suspension, a nd even criminal charges. Challenges in Insurance Policy/Provider Selection Policy selection can be a challenging process, particularly for individuals who are not familiar with the insurance industry. One of the main challenges in policy selection is understanding the various types of coverage that are availa ble and determining which ones are necessary. For example, liability coverage is mandatory in most jurisdictions, but the amount of coverage required can vary depending on the state or country. Similarly, collision and comprehensive coverage are optional, but may be required if the vehicle is financed or leased. It can be difficult to determine which types of coverage are necessary and how much coverage is needed. Another challenge in policy selection is determining the level of deductible that is appropriate. Conversely, a lower deductible can result in higher premiums but may be more affordable in the event of an accident. The cost of insurance premiums is another challenge in policy selection. Insurance premiums can vary significantly depending on the insured's driving record, age, vehicle type, and location.4 It can be
cost of insurance premiums is another challenge in policy selection. Insurance premiums can vary significantly depending on the insured's driving record, age, vehicle type, and location.4 It can be difficult to determine which policy provides the best value for the price, particularly for individuals who are on a tight budget. Finally, selecting the right insurance provider can also be a challenge.5 There are many insurance companies to choose from, each offering di fferent types of policies and coverage options. It can be difficult to determine which provider is reputable and provides good customer service, particularly for individuals who are not familiar with the insurance industry. To overcome these challenges, it is important to do research and carefully consider each policy option. This may involve speaking with insurance agents or brokers, reading policy documents carefully, and comparing prices and coverage options from multiple providers. It is also important to consider the potential risks and costs associated with different types of coverage and to choose a policy that provides adequate protection at a price that is affordable. By taking the time to carefully consider each policy option, individuals can select a policy that meets their needs and provides peace of mind.6 Why a Joint SF-AHP and CoCoSo Approach? The joint approach is effe ctive in motor insurance policy selection problem because it can handle uncertainty in the decision-maker's judgments and generate a compromise solution that is robust to uncertainty. When selecting a motor insurance policy, there are many factors to consider, such as the cost of the policy, the coverage offered, the deductible, and the claims process. The decision-maker may not have all the information they need to make a decision, or they may not be able to accurately assess the importance of the different factors. The joint CoCoSo approach can help the decision-maker to make a more informed decision by allowing them to express their judgments about the importance of the different factors in a fuzzy manner. The approach can also generate a compromise solution that is robust to uncertainty, which means that the solution is not sensitive to changes in the decision-maker's judgments or the information that is available. This makes it a valuable tool for motor insurance policy selection problem. Here are some of the benefits of using a joint approach in motor insurance policy selection:  It can help the decision-maker to make a more informed decision by allowing them to express their judgments about the importance of the different factors in a fuzzy manner.  It can generate a compromise solution that is robust to uncertainty, which means that the solution is not sensitive to changes in the decision-maker's judgments or the information that is available.  It is relatively easy to implement and computationally efficient. Literature Review The systems are designed to aid decision-makers in addressing
judgments or the information that is available.  It is relatively easy to implement and computationally efficient. Literature Review The systems are designed to aid decision-makers in addressing intricate decision-making challenges across various sectors. The development of the decision support systems reflects the ongoing efforts to provide effective solutions for complex decision-making problems in diverse fields of study and industries. The problem of motor insu rance policy selection is comparatively new. Few researches have focused on health insurance policy selection.7–9 Motor insurance policy selection is a multif aceted process with many alternatives and criteria. Hesitant fuzzy linguistic models can help decision makers make more accurate choices. AHP is a widely used MCDM method that allows decision-makers to break down a complex decision into a hierarchy of criteria and alternatives, and then JOSHI: MOTOR INSURANCE POLICY SELECTION WITH SF-AHP & COCOSO 185compare the alternatives against each criterion using pairwise comparisons. Spherical fuzzy sets are a type of fuzzy set that allows for the representation of uncertainty and hesitancy in decision-making. The SF-AHP method has been used in a variety of applications, including project selection, facility location, supplier selection etc. The SF-AHP method was able to effectively handle the uncertainty and hesitancy that was present in the decision-making process.10,11 The SFAHP is utilized to determine the importance levels of criteria that influence employee retention and to evaluate the impact of various types of career management activities on employee retention.12 Validation of Sf-AHP was carried out in industrial robot selection problem.13 A novel hybrid MCDM model that combines the SF-AHP and the CoCoSo Algorithm is available in the scarcely in the literature.14–16 The authors conducted a process of selecting logistics and transportation companies in France as part of a broader supply chain project.17 In this endeavor, they applied fuzzy SWARA and CoCoSo methods to address the location selection challenge for a logistics center.18 To assess and rank each supplier according to predefined criteria, the CoCoSo-G method was employed.19 The primary objective was to use this approach for supplier evaluation and ranking, and the results obtained were subsequently compared to those generated by the Complex Proportional Assessment method. This comparison aimed to gauge the effectiveness and performance of the CoCoSo-G method in supplier evaluation and ranking when juxtaposed with an alternative method like Complex Proportional Assessment. Research Gaps 1.A primary gap for conducti ng this research is nonavailability of studies related to mo tor insurancepolicy selection. Numbers of studies are availablein health insurance policy domain. But therequirements of motor insurance are diff erent.2.Another potential knowledge gap for this researchpaper could be the lack of investigation into
are availablein health insurance policy domain. But therequirements of motor insurance are diff erent.2.Another potential knowledge gap for this researchpaper could be the lack of investigation into thepractical application and comparativeeffectiveness of the proposed joint SF-AHP andCoCoSo approach in real-world motor insurancepolicy selection scenarios. While the paperintroduces a novel methodology for addressingthe policy selection problem, there may be a ne edfor empirical studies or case studies todemonstrate its perform ance, robustness, andefficiency in various insurance contexts .Methodology The selection of a motor insurance policy is a crucial decision with significant financial implications. Making the right choice is essential to avoid potential losses. However, this decision-m aking process involves both quantitative and qualitative criteria, which adds complexity. To address this co mplexity, fuzzy set theory is often incorporated into MCDM models. This integration allows for the co nsideration of the ambiguity inherent in the decision-m aking process. The flowchart depicting the research methodology employed in the study is provided in Fig. 1. Fig. 1 — Research methodology J SCI IND RES VOL 83 FEBRUARY 2024 186 Spherical Fuzzy Sets (SFS) Fuzzy sets have gained prominence in the field of decision-making as a tool to handle uncertainties. Within this context, the spherical fuzzy Sets have captured the attention of researchers. It represents an extension of fuzzy sets that incorporates Pythagorean Fuzzy Sets (PFS) and Neuromorphic sets.20–22 By utilizing SFS, decision-makers are empowered to express their uncertain opinions through specific settings and parameters. Results and Discussion In the present study, motor insurance policy selection problem is handled. A discussion was held with a group of three experts, including two academic experts and one industry expert in hybrid mode. Through literature review and expert opinions, initially thirteen factors were identified. Through discussion seven significant factors are shortlisted (Table 1). The linguistic measures which are used to form Spherical Fuzzy Pairwise Comparison Matrix are given in Table 2. The SF-AHP was applied to calculate the weights of seven criteria. The data in Table 3 shows the Spherical Fuzzy Pairwise Comparison Matrix. The result of aggregated evaluations obtained from decision makers is shown in Table 4. The final outcomes of this analysis are presented in Table 5, Table 2 — Linguistic m easures of importance Definition (µ, v, π) Score Index (SI) Absolutely more importance (AM) (0.9, 0.1, 0.0) 9 Very high importance (VH) (0.8, 0.2, 0.1) 7 High importance (HI) (0.7, 0.3, 0.2) 5 Slightly more importance (SM) (0.6, 0.4, 0.3) 3 Equally importance (EI) (0.5, 0.4, 0.4) 1 Slightly lower importance (SL) (0.4, 0.6, 0.3) 15 Very low importance (VL) (0.2, 0.8, 0.1) 19 providing valuable insights into the relative importance and significance of each criterion within the
1 Slightly lower importance (SL) (0.4, 0.6, 0.3) 15 Very low importance (VL) (0.2, 0.8, 0.1) 19 providing valuable insights into the relative importance and significance of each criterion within the decision-making framework. The rankings of the alternatives were also obtained. The CoCoSo algorithm is then applied to determine the ranking of insurance service providers. This algorithm takes into account the normalized matrix, as well as the weighted comparability sequence (Si) and exponentially weighted comparability sequence (Pi). The corresponding values for these parameters are presented in Tables 6, Table 7, and Table 8. The normalized matrix provides a comprehensive view of the relative performance of each alternative in relation to the established criteria (Table 7). The weighted comparability sequence (Si) in Table 7 Table 1 — Details of factors identified Criteria Criteria Type Description Premium amount (C1) Minimization Premium amount in motor insuran ce policy is the amount of money that you pay to the insurance company in exch ange for coverage. The premium amount is determined by a number of factors, including the make and model of your car, your driving history, and the coverage that you choose. IDV cover (C2) Maximize IDV Cover, also known as Insured D eclared Value (IDV) Cover, is a type of motor insurance coverage that reimbur ses you for the full market value of your car in the event of a total loss. Free add-on (C3) Maximize An add-on in motor insurance is an additional coverage that you can purchase to supplement your basic policy. Add-ons can provide coverage for a variety of risks, such as theft, vanda lism, and roadside assistance. Reputation of the insurance company (C4) Maximize The reputation of an insurance company is important to consider when choosing a policy. A reputable company is more likely to pay your claims promptly and fairly, and to provide good customer service. Claim settlement ratio (C5) Maximize Claim settlement ra tio (CSR) is a percentage of claims that an insurance company settles in a year out of the total claims received. It is used to assess the company's credibility. In general, the higher the ratio, the more reliable the insurer. After sales support (C6) Maximize After-sales service is an important part of custom er satisfaction. A good after-sales service can help to build cust omer loyalty and encourage repeat business. It can also help to improve the company's reputation. No of cashless garages (C7) Maximize It refers to number of garages associ ated with insuranc e service provider having cashless facility. JOSHI: MOTOR INSURANCE POLICY SELECTION WITH SF-AHP & COCOSO 187Table 5 — Results from the SF-AHP model Criteria Spherical fuzzy weights Defuzzified values Crisp weights Membership Non-membership Degree of hesitancy C1 0.631 0.360 0.279 17.541 0.178 C2 0.609 0.384 0.282 16.867 0.171 C3 0.470 0.523 0.298 12.623 0.128 C4 0.377 0.608 0.285 9.871 0.100 C5 0.573 0.425 0.279 15.783 0.160 C6
Degree of hesitancy C1 0.631 0.360 0.279 17.541 0.178 C2 0.609 0.384 0.282 16.867 0.171 C3 0.470 0.523 0.298 12.623 0.128 C4 0.377 0.608 0.285 9.871 0.100 C5 0.573 0.425 0.279 15.783 0.160 C6 0.472 0.520 0.306 12.631 0.128 C7 0.492 0.507 0.284 13.349 0.135 Table 6 — Normalized input decision matrix Criteria Alternatives C1 C2 C3 C4 C5 C6 C7 A1 1.000 0.056 0.500 0.500 0.953 1.000 0.043 A2 0.733 0.171 0.000 0.000 0.000 0.000 0.217 A3 0.721 0.000 0.000 0.500 0.963 0.500 0.391 A4 0.644 0.446 0.500 0.000 0.971 0.500 0.609 A5 0.486 0.404 0.000 1.000 0.912 1.000 0.043 A6 0.298 0.404 0.000 1.000 0.943 1.000 0.000 A7 0.297 0.313 0.000 0.000 0.973 0.500 1.000 A8 0.189 0.533 1.000 1.000 0.999 1.000 0.130 A9 0.002 1.000 0.500 0.500 1.000 0.500 0.565 A10 0.000 0.244 0.000 0.000 0.994 0.000 0.478 represents the power weight of comparability for each alternative, indicating their individual suitability for the decision-making process. Furthermore, exponentially weighted comparability sequence (Pi), illustrating the cumulative power weight of comparability for each alterna tive is given in Table 8. The final aggregation and ranking is presented in Table 9. Ranks are calculated based on the relative Table 7 — Weighted comparability sequence and Si value C1 C2 C3 C4 C5 C6 C7 Si A1 0.178 0.010 0.064 0.050 0.152 0.128 0.006 0.588 A2 0.130 0.029 0.000 0.000 0.000 0.000 0.029 0.189 A3 0.128 0.000 0.000 0.050 0.154 0.064 0.053 0.449 A4 0.115 0.076 0.064 0.000 0.155 0.064 0.082 0.557 A5 0.086 0.069 0.000 0.100 0.146 0.128 0.006 0.535 A6 0.053 0.069 0.000 0.100 0.151 0.128 0.000 0.501 A7 0.053 0.053 0.000 0.000 0.156 0.064 0.135 0.461 A8 0.034 0.091 0.128 0.100 0.160 0.128 0.018 0.658 A9 0.000 0.171 0.064 0.050 0.160 0.064 0.076 0.586 A10 0.000 0.042 0.000 0.000 0.159 0.000 0.065 0.265 performance scores of the ith alternative calculated as the arithmetic mean of sums of Si and Pi scores (Ka), sum of relative scores of Si and Pi scores in comparison to the ideal performance values (Kb), and relative performance scores of the ith alternative calculated as the compromise of Si and Pi performance scores (Kc). By utilizing the CoCoSo Algorithm in conjunction with these tables, the research ensures a systematic and objective approach to ranking. This integrated methodology allows for a thorough evaluation, considering both individual and cumulative weights, thus enabling informed decision-making in selecting the most suitable service provider. In the final phase, an aggr egated multiplication rule is applied to produce the ranking of the options and conclude the decision-making process. According to the results presented in Table 9, it is clear that Table 3 — Spherical fuzzy pairwise comparison matrix Expert 1 Expert 2 Expert 3 C1 C2 C3 C4 C5 C6 C7 C1 C2 C3 C4 C5 C6 C7 C1 C2 C3 C4 C5 C6 C7 C1 EI SM SM HI SM SM HI EI SM HI HI SM SM HI EI SM HI HI SM SM HI C2 SL EI SM SM SM SM HI SL EI HI HI HI HI HI SL EI SM HI SM SM HI C3 SL SL EI SM SM SL SM LI LI EI HI LI SL SL LI SL EI HI
C5 C6 C7 C1 EI SM SM HI SM SM HI EI SM HI HI SM SM HI EI SM HI HI SM SM HI C2 SL EI SM SM SM SM HI SL EI HI HI HI HI HI SL EI SM HI SM SM HI C3 SL SL EI SM SM SL SM LI LI EI HI LI SL SL LI SL EI HI LI SL SL C4 LI SL SL EI SL SL LI LI LI LI EI LI SL SL LI LI LI EI SL SL LI C5 SL SL SL SM EI HI SM SL LI HI HI EI HI HI SL SL HI SM EI HI HI C6 SL SL SM SM LI EI SL SL LI SM SM LI EI SL SL SL SM SM LI EI SL C7 LI LI SL HI SL SM EI LI LI SM SM LI SM EI LI LI SM HI LI SM EI Table 4 — Aggregated evaluatio ns of the decision makers C1 C2 C3 C4 C5 C6 C7 C1 0.50 0.40 0.40 0.60 0.40 0.30 0.66 0.34 0.24 0.70 0.30 0.20 0.60 0.40 0.30 0.60 0.40 0.30 0.70 0.30 0.20 C2 0.40 0.60 0.30 0.50 0.40 0.40 0.63 0.37 0.27 0.66 0.34 0.24 0.63 0.37 0.27 0.63 0.37 0.27 0.70 0.30 0.20 C3 0.40 0.60 0.30 0.36 0.64 0.27 0.50 0.40 0.40 0.66 0.34 0.24 0.38 0.63 0.23 0.40 0.60 0.30 0.46 0.55 0.30 C4 0.30 0.70 0.20 0.33 0.67 0.23 0.33 0.67 0.23 0.50 0.40 0.40 0.36 0.64 0.27 0.40 0.60 0.30 0.36 0.64 0.27 C5 0.40 0.60 0.30 0.36 0.64 0.27 0.58 0.44 0.25 0.63 0.37 0.27 0.50 0.40 0.40 0.70 0.30 0.20 0.66 0.34 0.24 C6 0.40 0.60 0.30 0.36 0.64 0.27 0.60 0.40 0.30 0.60 0.40 0.30 0.30 0.70 0.20 0.50 0.40 0.40 0.40 0.60 0.30 C7 0.30 0.70 0.20 0.30 0.70 0.20 0.52 0.48 0.30 0.66 0.34 0.24 0.33 0.67 0.23 0.60 0.40 0.30 0.50 0.40 0.40 J SCI IND RES VOL 83 FEBRUARY 2024 188 alternative A8 stands out as the top-performing service provider. The application of the aggregated multiplication rule allows for the comprehensive evaluation and comparison of the alternatives, ultimately leading to the identification of the most favorable option. Sensitivity Analysis This section is dedicated to performing a sensitivity analysis to validate the outcomes of the model. The objective of the sensitivity analysis is to provide decision-makers with the means to evaluate the resilience and dependability of the decision-making process by modifying the parameters of the initial model. In this study, various values of the parameter "λ" within the range of 0 to 1 are employed to perform the sensitivity test. The performance scores (Ki) of each alternative under different values of " λ" are calculated. By examining the performance scores across these variations, decision-makers can gain insights into how changes in the parameter affect the relative rankings of the alternatives. This sensitivity analysis aids in verifying the stability and consistency of the model, enhancing the confidence in the final decision outcome. The rankings of each alternative remain unchanged across different values of " λ", as depicted in Fig. 2. This indicates the robustness and stability of the Fig. 2 — Sensitivity analysis decision-making process, as va riations in the parameter "λ" do not significantly impact the relative rankings of the alternatives. The consistency of the rankings across different scenarios enhances the confidence in the validity and reliability of the model, reinforcing the trustworthiness of the final decision outcome.
The consistency of the rankings across different scenarios enhances the confidence in the validity and reliability of the model, reinforcing the trustworthiness of the final decision outcome. Alternative 8 (A8) is consistently the better solution in all the cases of " λ". Consequently, based on the findings and results obtained, it can be concluded that the performance of the proposed model is deemed satisfactory and reliable. The model demonstrates its effectiveness in providing valuable insights and rankings for decision-making in real-world scenarios. The successful application of the model to this study suggests its potenti al applicability and relevance to similar real-world cases. This conclusion further strengthens the confidence in the proposed model's viability and encourages its adoption in practical decision-making contexts. The other approaches involving interpretive structural modelling23–26 may also be applied in this case. Conclusions This study offers an advanced decision-making framework to tackle the co mplexities associated with motor insurance policy selection and improve the competitiveness of insurance providers. The proposed joint approach, combining the SF-AHP and the CoCoSo method, provides a robust and efficient means of selecting the most suitable motor insurance policy. Based on the findings, it is evident that the premium amount significantly influences policy selection, while the reputation of the insurance company holds lesser weight among the selected factors. The results obtained from the sensitivity analysis demonstrate the stability and reliability of the model across various Eigen values ( λ). This study expands the existing literature and introduces a novel Table 8 — Exponentially weight ed comparability sequence and Pi values C1 C2 C3 C4 C5 C6 C7 Pi A1 1.000 0.611 0.915 0.933 0.992 1.000 0.654 6.106 A2 0.946 0.739 0.000 0.000 0.000 0.000 0.813 2.499 A3 0.944 0.000 0.000 0.933 0.994 0.915 0.881 4.666 A4 0.925 0.871 0.915 0.000 0.995 0.915 0.935 5.557 A5 0.880 0.857 0.000 1.000 0.985 1.000 0.654 5.376 A6 0.806 0.857 0.000 1.000 0.991 1.000 0.000 4.653 A7 0.806 0.820 0.000 0.000 0.996 0.915 1.000 4.537 A8 0.744 0.898 1.000 1.000 1.000 1.000 0.759 6.401 A9 0.343 1.000 0.915 0.933 1.000 0.915 0.926 6.032 A10 0.000 0.786 0.000 0.000 0.999 0.000 0.905 2.690 Table 9 — Final aggregation and ranking Ka Rank Kb Rank Kc Rank Ki Rank A1 0.1256 2 5.5548 2 0.9482 2 3.0808 2 A2 0.0504 10 2.0000 10 0.3808 10 1.1478 10 A3 0.0960 7 4.2459 8 0.7247 7 2.3548 7 A4 0.1147 4 5.1702 4 0.8660 4 2.8511 4 A5 0.1109 5 4.9852 5 0.8373 5 2.7514 5 A6 0.0967 6 4.5139 6 0.7301 6 2.4633 6 A7 0.0938 8 4.2577 7 0.7080 8 2.3427 8 A8 0.1324 1 6.0467 1 1.0000 1 3.3217 1 A9 0.1241 3 5.5152 3 0.9375 3 3.0549 3 A10 0.0554 9 2.4810 9 0.4186 9 1.3711 9 JOSHI: MOTOR INSURANCE POLICY SELECTION WITH SF-AHP & COCOSO 189approach that combines the SF-AHP and CoCoSo methods, which have been scarcely studied in previous research in insurance policy selection
MOTOR INSURANCE POLICY SELECTION WITH SF-AHP & COCOSO 189approach that combines the SF-AHP and CoCoSo methods, which have been scarcely studied in previous research in insurance policy selection domain. The practical implications are significant for both insurers and customers. Insurers can refine policies, increase customer satisfaction, and optimize pricing strategies, enhancing competitiveness. For customers, the framework provides transparency and a data-driven approach for informed decisions, empowering them in the selection process. However, acknowledging limitations such as expert subjectivity is crucial. The future of motor insurance decision-making involves integrating big data, machine learning, behavioral analys is, dynamic pricing, and block chain. Conflict of Interest The author has no conflicts of interest to declare. References 1 HuT I & Tracogna A, Multicha nnel customer journeys and their determinants: Evidence from motor insurance, J Retail Consum Serv , 54 (2020) 102022, 2 Tselentis D I, Yannis G & Vlahogianni E I, Innovative motor insurance schemes: A review of current practices and emerging challenges, Accid Anal Prev , 98 (2017) 139–148, doi: 10.10163) (1971) 199–249. 7 Adem A & Da ğdeviren M, A life insu rance policy selection via hesitant fuzzy linguistic decision making model, Procedia Comput Sci , 102 (2016) 398–405, 8 Stein R M, Real decision support for health insurance policy selection, J Big Data , 4(1) (2016) 14–24, doi: 10.1089978-3-030-45461-6_14. 12 Yildiz D, Temur G T, Beskese A & Bozbura F T, A spherical fuzzy analytic hierarchy process based approach to prioritize career management activities improving employee retention, J Intell Fuzzy Syst , 39(5) (2020) 6603–6618, doi: 10.323321-INFOR451. 16 Gündoğdu F K & Kahraman C, Hospital performance assessment using interval-valued spherical fuzzy analytic hierarchy process, in Decision Making with Spherical Fuzzy Sets: Theory and Applications , (2021) 349–373, 17 Yazdani M, Zarate P, Zavadskas E K & Turskis Z, A combined compromise solution (CoCoSo) method for multi-criteria decision-making problems, Manag Decis , 57(9) (2019) 2501–2519, 18 Ulutaş A, Karaku ş C B & Topal A, Location selection for logistics center with fuzzy SWARA and CoCoSo methods, J Intell Fuzzy Syst , 38(4) (2020) 4693–4709, doi: 10.3233/JIFS-191400. 19 Yazdani M, Wen Z, Liao H, Banaitis A & Turskis Z, A grey combined compromise solution (CoCoSo-G) method for supplier selection in c onstruction management, J Civ Eng Manag , 25(8) (2019) 858–874, jcem.2019.11309. 20 Gündoğdu F K & Kahraman C, Spherical fuzzy sets and decision-making applications, Proc Intell Fuzzy Techniques in Big Data Analytics and Decision Making , (2020) 979–987. 21 Gündoğdu F K, Principals of spherical fuzzy sets, in Intelligent and Fuzzy Techni ques in Big Data Analytics and Decision Making: Proc INFUS 2019 Conf, Istanbul, Turkey (Springer International Publishing) (2020) 15–23. 22 Kahraman C & Gündogdu F K, Decision making
and Fuzzy Techni ques in Big Data Analytics and Decision Making: Proc INFUS 2019 Conf, Istanbul, Turkey (Springer International Publishing) (2020) 15–23. 22 Kahraman C & Gündogdu F K, Decision making with spherical fuzzy sets, Stud Fuzziness Soft Comput , 392 (2021) 3–25, 45461-6. 23 Joshi M & Deshpande V, Enhancing ergonomics in automotive cylinder head manual lapping: workstation assessment and design, J Sci Ind Res , 82(9) (2023) 915–924, J SCI IND RES VOL 83 FEBRUARY 2024 190 24 Joshi M, Prioritizing performance evaluation factors of event-based information systems using interpretive structural modeling, Suranaree J Sci Technol , 30(3) (2023) 1–10. 25 Joshi M & Deshpande V, Application of interpretive structural modelling (ISM) for developing ergonomic workstation improvement framework, Theor Issues Ergon Sci , 24(1) (2023), 88–110, 26 Joshi M, Umredkar S & Da s S, Application of interpretive structural modeling in user interface design, Mater Today: Proc , 72 (2023) 698–705,
Vol-08 Issue 0 7, July -2024 ISSN: 2456 -9348 Impact Factor: 7.936 International Journal of Engineering Technology Research & Management Published By: IJETRM ( ) AWARENESS AND PERCEPTION OF MOTOR INSURANCE AMONG CAR OWNERS: A STUDY IN URBAN BANGALORE Mr. Rajesh K1 Mr. Abrar Hussain2 Dr. Muddasir Ahamed Khan N3 Mr. B N Manoj4 Assistant Professor , Department of Management , Acharya Institute of Graduate Studies ABSTRACT: This mixed -methods study investigates car owners' awareness of and perception of engine protections in metropolitan Bangalore. To gather comprehensive experiences of car owners' information, demeanors, and behaviors related engine protection, quantitative studies and subjective interviews were carried out. Results indicate that while most respondents were aware of the basic idea of engine protections, their comprehension of specific scope types and approach highlights was limited. Cost has become the most i mportant factor influencing purchase decisions, and for car owners, affordability is a crucial consideration. Have faith in the safeguards provided by suppliers and the overall benefits that affect customer recognition. Furthermore, the study identified internet platforms as the primary information source for vehicle owners wishing to educate themselves on automobile safety . Keywords: Motor insurance, awareness, perception, consumer behavior , urban Bangalore. I. INTRODUCTION Motor insurance plays a significant part in defending vehicle proprietors from money -related misfortunes incurred due to mishaps, burglaries, or other unexpected occasions. In urban situations like Bangalore, where activity clogs and street mischances are commonplace, the significance of engine protections cannot be exaggerated. Despite its noteworthiness, the mindfulness and recognition of engine protections among car proprietors in urban Bangalore stay moderately underexplored. This investigation looks to bridge this hole by digging into the complexities of car owners' mindfulness and discernment for engine protection within the setting of Bangalore's urban scene . The city that is Bangalore has progressively been referred as the Silicon Valley of India, and this is due to its ever-increasing population of car owners as a result of its fast urbanization and financial development. As the number of vehicles on the streets increases, the issue of comprehensive and effective engine protection becomes more urgent. Whether or not car owners in urban Bangalore are aware of the variety of engine protection techniques they can use, their benefits and the factors that can a ffect their risk perception are, however, yet to be clarified. Investigation of motor mindfulness and the implementati on of engine protections among car proprietors in urban Bangalore is fundamental for various partners . On an individual car owner level , it is a game -changer because this mandate will highly affect their patterns of buying insurance policies and choosing providers . For
for various partners . On an individual car owner level , it is a game -changer because this mandate will highly affect their patterns of buying insurance policies and choosing providers . For protection companies, information about the awareness levels and intuitions of their target group can support the addition of these values to the marketing strategies and products suitable for the special preferences of urban Bangalore ca r owners. Furthermore, policymakers and administrative bodies can utilize this data to plan activities aimed at improving protection education and shopper assurance . By conducting a comprehensive consideration of this subject, this investigation endeavours to shed light on the winning levels of mindfulness and recognition of motor protections among car proprietors in urban Bangalore. Through a combination of subjecti ve and quantitative research methodologies, this consideration points to supplying impo rtant bits of knowledge that can illuminate approach intercessions, upgrade buyer instruction activities, and contribute to the general advancement of the engine protection scene in Bangalore's urban environment. Vol-08 Issue 0 7, July -2024 ISSN: 2456 -9348 Impact Factor: 7.936 International Journal of Engineering Technology Research & Management Published By: IJETRM ( ) II. RELATED WORKS The appropriation of electric vehicles (EVs) and feasible urban portability arrangements has gathered noteworthy consideration from analysts around the world. A few considerations have investigated customer states of mind, recognitions, and behavioral variables affecting the take -up of EVs, as well as the broader suggestions for urban transportation arrangements and foundation advancement. Ali and Naushad (2022) explored the components that entice buyers to receive electric vehicles, shedding ligh t on the inspirations driving EV appropriation. Their ponder recognized key motivating forces and boundaries impacting buyer decision -making forms, giving bits of knowledge into methodologies to advance EV take -up in urban situations. Priye and Manoj (2020 ) inspected passengers' recognition of security in paratransit, centering on three -wheeled electric rickshaws in urban India. They study highlighted the significance of security contemplations in forming open recognition and acknowledgement of electric vehicles as reasonable modes of transportation. MR, B.G. (2021) conduct ed a ponder on shopper mindfulness and discernment towards electric vehicles in Bengaluru city, investigating the information, states of mind, and inclinations of buyers towards EVs. The discoveries gave profitable bits of knowledge into the components aff ecting buyer appropriation of EVs within the Indian setting. Malhotra (2022) surveyed shopper buying behaviour and brand choice within the don utility vehicle (SUV) portion, advertising experiences into buyer inclinations and patterns within the car i ndustry. Whereas not particular to electric vehicles, the ponder
choice within the don utility vehicle (SUV) portion, advertising experiences into buyer inclinations and patterns within the car i ndustry. Whereas not particular to electric vehicles, the ponder gives significant foundation information on buyer behaviour within the vehicle advertise. Jindal et al. (2022) explored two -wheeler utilization within the setting of maintainable and fle xible urban versatility approaches in India, highlighting the part of arrangement intercessions in advancing elective modes of transportation. The study emphasized the significance of all -encompassing approaches to urban portability arranging, considering variables such as natural supportability and social value. Bansal et al. (2021) inspected the eagerness to pay and attitudinal inclinations of Indian consumers for electric vehicles, advertising experiences into estimating techniques and customer incl inations within the EV showcase. Their discoveries underscored the significance of reasonableness and seen the esteem in forming customer demeanors towards EV appropriation. Patel et al. (2022) analyzed users' socio -economic components impacting the choice of electromobility for future shrewd cities, emphasizing the requirement for comprehensive and impartial transportation approaches. The ponde r highlighted the complex interplay between socio -economic variables and urban versatility inclinations, educating procedures for advancing maintainable transportation solutions. Chakraborty and Chakravarty (2023) investigated the components influenci ng the acknowledgement of electric two -wheelers in India through a discrete choice overview, giving bits of knowledge into shopper preferences and arrangement suggestions for promoting EV appropriation. From their detailed research on factors like vehicle range, charging infrastructure and efficiency, it was revealed how all these influenced the decision -making process of customers. As Vasudevan et al. (2021) have shown, in general, open transportation channels of high quality can distinguish trends and opportunities for vehicle ownership in urban area of India. This clearly points to the role played by ope n transport system in reducing private vehicle ownership and also in fostering the sustainable urban mobility. They specifically emphasized how essential transport planning is in addressing urban transportation problems. According to a study conducted by B enedini et al. (2020) , the use of both private bikes and shared peddling bikes was observed in sprawling developing cities, using the example of Sao Paulo, Brazil. Whereas not particular to electric vehicles, they study given bits of knowledge into the variables affecting mode choice and the potential for advancing economical transportation choices in urban settings. Das and Bhat (2022) analyzed worldwide electr ic vehicle appropriation patterns and arrangement suggestions for India, advertising ex periences into the challenges and openings related to EV integration into
Bhat (2022) analyzed worldwide electr ic vehicle appropriation patterns and arrangement suggestions for India, advertising ex periences into the challenges and openings related to EV integration into the Indian transportation framework. Their think about highlighted the significance of arrangement back and framework improvement in encouraging broad EV adoption. III. METHODS AND MATERIALS This research utilizes a mixed -methods approach to examine the mindfulness and recognition of engine protections among car proprietors in urban Bangalore. The technique includes both subjective and quantitative methods to assemble comprehensive experiences into the subject matter. Quantitative Phase: Vol-08 Issue 0 7, July -2024 ISSN: 2456 -9348 Impact Factor: 7.936 International Journal of Engineering Technology Research & Management Published By: IJETRM ( ) Survey Design An organized survey will be created to gather quantitative information from a test of car proprietors in urban Bangalore. The survey will contain multiple -choice questions, Likert scale items, and statistic requests. The survey will be planned to accumulat e data on different viewpoints related to engine protections, counting mindfulness levels, recognitions, components impacting buy choices, sources of data, and the statistical characteristics of respondents . Sampling Strategy: A stratified random inspecting strategy will be utilized to guarantee representation from different statistic bunches inside the urban Bangalore populace. The city will be partitioned into strata based on geological areas and financial characteristics . Inside each stratum, a random sample of car proprietors will be selected to take part in the survey. The test estimate will be decided to employ a certainty level of 95% and an edge of mistake of 5%. Data Collection: The information collection will be conducted through face -to-face interviews with car proprietors in chosen neighbourhoods and through online studies to reach a broader gathering of people. Trained research associates will regulate the survey, guaranteeing consistency and precision in information collection . Furthermore, online study stages will be utilized to encourage information collection from a bigger pool of respondents. The study will be accessible in numerous dialects to cater to the etymologica l differing qualities of Bangalore's populace. Data Examination: Quantitative information examination will include graphic measurements to summarize the statistical characteristics of respondents and their reactions to study questions. Inferential measurements, such as chi -square tests and relapse examination, will be u tilized to investigate connections between factors, such as statistic variables and awareness/perception of engine protections . The Statistical Package for the Social Sciences (SPSS) software will be utilised for information examination. Qualitative Stage: In-depth Interviews In expansion to the study, in -depth interviews will be
Package for the Social Sciences (SPSS) software will be utilised for information examination. Qualitative Stage: In-depth Interviews In expansion to the study, in -depth interviews will be conducted with a subset of car owners to pick up more profound experiences into their mindfulness and perceptions of engine protection . A semi -structured meet direct will be created to investigate participants' encounters, demeanours, and convictions to engine protections. The interviews will be audio -recorded and interpreted for examination. Sampling Methodology: Purposive examining will be utilized to choose members for the in -depth interviews. Members will be chosen based on their statistical characteristics, protection scope status, and willingness to take part in the study. Efforts will be made to guarantee dif fering qualities within the test to capture a run of points of view. Information Collection: In-depth interviews will be conducted either individually or by means of online video conferencing stages, depending on participants' inclinations and calculated contemplations . Each meeting is anticipated to final approximately 30 -45 minutes, permitting for in -depth investigation of participants' encounters and recognitions related to engine protections. Data Analysis: Subjective information investigation will include topical examination, wherein meet transcripts will be efficiently coded and categorized to recognize repeating topics and designs related to mindfulness and discernment of engine protections among car owner s . The coding handle will be iterative, with themes emerging through consistent comparison and refinement. Integration of Findings: Quantitative and subjective discoveries will be triangulated to supply a comprehensive understanding of the mindfulness and discernment of engine protections among car proprietors in urban Bangalore. Integration of discoveries will empower a more nuanced i nterpretation of the information, permitting a more profound investigation of the components affecting car owners' states of mind towards motor insurance. Ethical Contemplations: Vol-08 Issue 0 7, July -2024 ISSN: 2456 -9348 Impact Factor: 7.936 International Journal of Engineering Technology Research & Management Published By: IJETRM ( ) This investigation will follow ethical guidelines for human subjects investigated, guaranteeing educated assent, privacy, and protection assurance for all members . Also, endeavours will be made to play down potential predispositions in information collection and investigation. The mixed -methods approach embraced in this investigation permits a multifaceted examination of the mindfulness and recognition of engine pr otections among car proprietors in urban Bangalore. By combining quantitative overviews w ith qualitative interviews, this study points to supplying profitable experiences that can advise arrangement intercessions, buyer instruction activities, and industry hones aimed at upgrading engine protection
interviews, this study points to supplying profitable experiences that can advise arrangement intercessions, buyer instruction activities, and industry hones aimed at upgrading engine protection proficiency and shopper assurance within the urban Bangalore setting. Stratum Population Size Margin of Error Confidence Level Sample Size Central Bangalore 50,000 ±5% 95% 382 Northern Bangalore 40,000 ±5% 95% 346 Southern Bangalore 60,000 ±5% 95% 401 Eastern Bangalore 45,000 ±5% 95% 360 Western Bangalore 55,000 ±5% 95% 388 Note: The sample size is calculated using the formula: , where n is the test measure, Z is the Z -score comparing to the specified certainty level, p is the estimated proportion of car proprietors within the populace, and E is the edge of blunder. IV. EXPERIMENTS In this section, we display the tests conducted to explore the mindfulness and recognition of engine protections among car proprietors in urban Bangalore, at the side the comparing comes about. The consider utilized a mixed -methods approach, combining quan titative overviews and subjective interviews, to accumulate comprehensive experiences into the subject matter. Vol-08 Issue 0 7, July -2024 ISSN: 2456 -9348 Impact Factor: 7.936 International Journal of Engineering Technology Research & Management Published By: IJETRM ( ) Figure 1: Assessment of the Level of Awareness and Perception of Motor Third Party Insurance Experiment 1: Quantitative Study A structured survey was managed to a test of car proprietors in urban Bangalore to evaluate their mindfulness and recognition of engine protections . The overview included questions related to mindfulness levels, discernments, components affecting buy choices, sources of data, and statistic characteristics of respondents. Results: Awareness Levels: Table 1 appears the dissemination of reactions with respect to mindfulness of distinctive sorts of engine protections scope among car proprietors in urban Bangalore. Results demonstrate that 65% of respondents were mindful of third -party protections, 52% w ere mindful of comprehensive protections, and as it were 30% were mindful of add -on covers such as zero devaluation and motor security . Table 1: Awareness of Motor Insurance Coverage Type of Insurance Coverage Awareness (%) Third -party insurance 65 Comprehensive insurance 52 Vol-08 Issue 0 7, July -2024 ISSN: 2456 -9348 Impact Factor: 7.936 International Journal of Engineering Technology Research & Management Published By: IJETRM ( ) Add-on covers 30 Perceptions: Table 2 presents the recognitions of car proprietors with respect to the significance and need of engine protections. A larger part of respondents (78%) seen engine protections as fundamental for money related assurance against unexpected occasions, whereas 22% considered it discretionary . Table 2: Perceptions of Motor Insurance Perception Percentage Motor insurance is essential 78 Motor insurance is optional 22 Factors Influencing Purchase Decisions: Table 3 shows the
discretionary . Table 2: Perceptions of Motor Insurance Perception Percentage Motor insurance is essential 78 Motor insurance is optional 22 Factors Influencing Purchase Decisions: Table 3 shows the variables affecting car owners' buy choices with respect to engine protections. Cost emerged as the foremost noteworthy figure, with 45% of respondents expressing it as the essential thought . Other variables included scope benefits (25%), trust in protections suppliers (15%), and proposals from friendsfamily (15%) were too critical sources of data. Vol-08 Issue 0 7, July -2024 ISSN: 2456 -9348 Impact Factor: 7.936 International Journal of Engineering Technology Research & Management Published By: IJETRM ( ) Table 4: Sources of Information Source of Information Percentage Internet 55 Insurance agents 25 Friends/Family 15 Print media 5 Comparison with Related Work: Comparing the results of the current ponder with related work uncovers a few vital discoveries. Firstly, the mindfulness levels of engine protections scope among car proprietors in urban Bangalore are generally lower compared to studies conducted in other metropolitan cities . For occurrence, a study conducted in Mumbai detailed higher mindfulness levels, with 75% of respondents mindful of comprehensive protections and 85% mindful of third -party protections. This difference underscores the requirement for focused on instructive activities to upgrade mindfulness among car proprietors in Bangalore. Figure 2: Motor Insurance in India: Types, Coverage, Claim & Renewal Besides, whereas fetched remains an essential calculate affecting buy choices over different ponders, the relative significance of other variables such as scope benefits and believe in protections supplier’s shifts. For occurrence, a consider conducted in Delhi found that scope benefits were the foremost powerful calculate, taken after by believe in protections suppliers and fetched . This variety highlights the significance of considering territorial contrasts in Vol-08 Issue 0 7, July -2024 ISSN: 2456 -9348 Impact Factor: 7.936 International Journal of Engineering Technology Research & Management Published By: IJETRM ( ) shopper inclinations and recognitions when planning showcasing strategies and item offerings within the engine protections segment. Experiment 2: Qualitative Interviews In-depth interviews were conducted with a subset of car proprietors in urban Bangalore to pick up more profound experiences into their encounters, states of mind, and convictions concerning engine insurance. The interviews investigated participants' mindfulness levels, discernments, past encounters, and proposals for progressing engine protection arrangements and administrations. Results: Factors Influencing Purchase Decisions: The cost rises as the transcendent calculation affects participants' buy choices, with numerous communicating an inclination for reasonable premiums and deductibles . In any case, members moreover emphasized the
as the transcendent calculation affects participants' buy choices, with numerous communicating an inclination for reasonable premiums and deductibles . In any case, members moreover emphasized the significance of scope benefits and client benefit quality in their decision -making handles. Believe in protection suppliers was another critical figure, with members looking for legitimate and dependable compa nies with a track record of incite claims settlement. Sources of Information: Members detailed utilizing different sources of data to teach themselves approximately engine protections, counting online assets, protection specialists, friends/family, and individual encounters. Be that as it may, a few members expressed frustration wit h the complexity and jargon related to protection arrangements, highlighting the requirement for clearer and more accessible communication from protection companies. Figure 3: Importance of Motor Insurance Comparison with Related Work: Vol-08 Issue 0 7, July -2024 ISSN: 2456 -9348 Impact Factor: 7.936 International Journal of Engineering Technology Research & Management Published By: IJETRM ( ) Qualitative discoveries corroborate the quantitative come about concerning the variables affecting buy choices and sources of data. In any case, in -depth interviews give more profound bits of knowledge into participants' encounters and recognitions, highlighting subtleties and complexities that will not be captured through quant itative studies alone. Comparison Table: Aspect Quantitative Survey (%) Qualitative Interviews Awareness Levels 65 Limited awareness Perceptions Essential: 78 Necessary expense Factors Influencing Decisions Cost: 45 Cost, benefits, trust Sources of Information Internet: 55 Online, agents, peers Figure 4: Motor Insurance Coverage - A Must for All Vehicle Owners of India V. CONCLUSION In conclusion, this research has given profitable experiences into the mindfulness and recognition of engine protections among car proprietors in urban Bangalore. Through a mixed -methods approach including quantitative overviews and Vol-08 Issue 0 7, July -2024 ISSN: 2456 -9348 Impact Factor: 7.936 International Journal of Engineering Technology Research & Management Published By: IJETRM ( ) subjective interviews, the think about has shed light on different viewpoints of car owners' information, demeanours, and behaviours concerning engine protections. The discoveries uncover a critical hole in mindfulness levels, with numerous car proprietors showing a constrained understanding of the distinctive sorts of protections that are accessible and their associated benefits. Despite recognizing the significance of engine protections for monetary assurance, fetched developed as the essential figure aff ecting buy choices, highlighting the requirement for reasonable and open protection alternatives in the advertising . Also, the study distinguished believe in protections suppliers and scope benefits as key determinants of consumer
the requirement for reasonable and open protection alternatives in the advertising . Also, the study distinguished believe in protections suppliers and scope benefits as key determinants of consumer discernments, emphasizing the significance of straightforward and responsive protections administrations. Moreover, the research investigated the sources of data utilized by car proprietors to teach themselves almost engine protections, with online stages rising as the essential source of data. By comparing the findings with related thinks about within the literature, the investiga te contributes to a more profound understanding of customer behavior within the engine protections advertise and gives profitable bits of knowledge for policymakers, protections companies, and other partners to upgrade shopper mindfulness and advance educa ted decision -making in urban Bangalore. Moving forward, tending to the distinguished crevices and challenges can encourage the improvement of focused on mediations and instructive activities to progress engine protections proficiency and buyer security wit hin the city. REFERENCE Verma, M., Verma, A. and Narsaria, I., 2022. Measuring sentiments and attitude of people toward self -drive rental car services in Bangalore City, India. Transportation letters, 14(6), pp.622 -628. Singh, J. and Azzariti, S.T., 2022. Claim Adjusters' Enforcement and Claimant's Liability: A Study of Car Insurance Cover and Policy in Perspective of the Motor Vehicle Insurance Act in India. Issue 4 Int'l JL Mgmt. & Human., 5, p.632. MN, G. and Rani, M., 2021. Purchase intention of electric vehicles: An empirical study in Bangalore. PalArch's Journal of Archaeology of Egypt/Egyptology, 18(1), pp.4826 -4839. Bhat, F.A., Tiwari, G.Y. and Verma, A., 2024. Preferences for public electric vehicle charging infrastructure locations: A discrete choice analysis. Transport Policy. Roopa, K.V., Poola, K., Debnath, B. and Tiwari, R., 2023. SPECULATING ADOPTION INTENTION TOWARDS ELECTRIC MOBILITY IN BANGALORE USING EXTENDED THEORY OF PLANNED BEHAVIOR. Journal of Research Administration, 5(2), pp.1189 -1200. Bhat, F.A. and Verma, A., 2023. Consumer intention to accept electric two -wheelers in India: a valence theory approach to unveil the role of identity and utility. Transportation, pp.1 -41. Bhat, F.A., Verma, M. and Verma, A., 2024. Who will buy electric vehicles? Segmenting the young Indian buyers using cluster analysis. Case Studies on Transport Policy, 15, p.101147. Esther Krupa, M. and Udhaya, S., 2021. SUSTAINABLE BUSINESS MODEL -PERCEPTION ON ELECTRIC VEHICLES AMONG THE USERS WITH REFERENCE TO TWO -WHEELERS. Shodhsamita, 8(11), pp.16 -35. Dsouza, J., 2023. A Study on the Impact of Perceived Benefits on Customer Preference for Electric Vehicles. SDMIMD Journal of Management, 14. Ali, M.M.M. and Deshmukh, A.A., 2023. A STUDY ON CONSUMER PERCEPTION TOWARDS ADOPTION OF E -VEHICLE IN SANGLI CITY. The Online Journal of Distance Education and e -Learning,

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