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Let $b,c$ be positive integers, $x_1,x_2$ be indeterminates over $\Z$ and $x_m, m \in \mathbb Z$ be rational functions defined by $x_{m-1}x_{m+1}=x_m^b+1$ if $m$ is odd and $x_{m-1}x_{m+1}=x_m^c+1$ if $m$ is even. In this short note, we prove that for any $m,k \in \Z$, $x_k$ can be expressed as a substraction-free Lau...
The quaternion equation X^n=A is solved for any integer number n > 1. A is a given quaternion with komplex numbers as its elements.
In this paper we extend some results obtained by Artamonov and Sabitov for quantum polynomials to skew quantum polynomials and quasi-commutative bijective skew PBW extensions. Moreover, we find a counterexample to the conjecture proposed in [6]
In this paper, we define a new cohomology theory for multiplicative Hom-pre-Lie algebras which controls deformations of Hom-pre-Lie algebra structure. This new cohomology is a natural one by considering the structure map.
We describe all possible coactions of finite groups (equivalently, all group gradings) on two-dimensional Artin-Schelter regular algebras. We give necessary and sufficient conditions for the associated Auslander map to be an isomorphism, and determine precisely when the invariant ring for the coaction is Artin-Schelte...
Let $A$ be a truncated polynomial ring over a complete discrete valuation ring $\mathcal{O}$, and we consider the additive category consisting of $A$-lattices $M$ with the property that $M\otimes \mathcal{K}$ is projective as an $A\otimes \mathcal{K}$-module, where $\mathcal{K}$ is the fraction field of $\mathcal{O}$. ...
We develop the general Theory of Cayley Hamilton algebras and we compare this with the theory of pseudocharacters. We finally characterize prime $T$--ideals for Cayley Hamilton algebras and discuss some of their geometry.
Let $A$ be a sheaf of Azumaya algebras over a Noetherian base $S$. In this paper we describe using generalized Severi-Brauer varieties, a quasi-projective moduli space parametrizing sheaves of ètale subalgebras of $A$.
We show that a structural matrix algebra $A$ is isomorphic to the endomorphism algebra of an algebraic-combinatorial object called a generalized flag. If the flag is equipped with a group grading, an algebra grading is induced on $A$.
Sovereign loan portfolios of Multilateral Development Banks (MDBs) typically consist of only a small number of borrowers and hence are heavily exposed to single name concentration risk. Based on realistic MDB portfolios constructed from publicly available data, this paper quantifies the magnitude of the exposure to na...
The aim of this paper is to introduce a synthetic ALM model that catches the main specificity of life insurance contracts. First, it keeps track of both market and book values to apply the regulatory profit sharing rule.
Predicting corporate default risk has long been a crucial topic in the finance field, as bankruptcies impose enormous costs on market participants as well as the economy as a whole. This paper aims to forecast frailty correlated default models with subjective judgements on a sample of U.S. public non-financial firms s...
We model systemic risk using a common factor that accounts for market-wide shocks and a tail dependence factor that accounts for linkages among extreme stock returns. Specifically, our theoretical model allows for firm-specific impacts of infrequent and extreme events.
We propose a risk measurement approach for a risk-averse stochastic problem. We provide results that guarantee that our problem has a solution.
This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss model...
The paper investigates the robust optimized certainty equivalents and analyzes the relevant properties of them as risk measures for loss positions with distribution uncertainty. On this basis, the robust generalized quantiles are proposed and discussed.
In this paper, we consider the pricing of derivative products that involve dynamic hedging strategies and payments within the planning horizon. Equity-indexed annuities (EIAs), Guaranteed investment certificate (GIC), American and Barrier options are typical examples of these products.
In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility.
Sustaining efficiency and stability by properly controlling the equity to asset ratio is one of the most important and difficult challenges in bank management. Due to unexpected and abrupt decline of asset values, a bank must closely monitor its net worth as well as market conditions, and one of its important concerns...
In most real scenarios the construction of a risk-neutral portfolio must be performed in discrete time and with transaction costs. Two human imposed constraints are the risk-aversion and the profit maximization, which together define a nonlinear optimization problem with a model-dependent solution.
In this paper, we obtain a property of the expectation of the inverse of compound Wishart matrices which results from their orthogonal invariance. Using this property as well as results from random matrix theory (RMT), we derive the asymptotic effect of the noise induced by estimating the covariance matrix on computin...
An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities and the banking/insurance/reinsurance industry. Koch (2017) introduced a notion of spatial risk measure and a corresponding set of axioms which are well suited to analyze the risk due to events having...
The purpose of this article is twofold. First, we motivate the need for a new type of stand-alone retirement income insurance product that would help individuals protect against personal longevity risk and possible "retirement ruin" in an economically efficient manner.
This paper investigates optimal investment and insurance strategies under a mean-variance criterion with path-dependent effects. We use a rough volatility model and a Hawkes process with a power kernel to capture the path dependence of the market.
Prudent management of insurance investment portfolios requires competent asset pricing of fixed-income assets with time-to-event contingent cash flows, such as consumer asset-backed securities (ABS). Current market pricing techniques for these assets either rely on a non-random time-to-event model or may not utilize d...
The Basel II internal ratings-based (IRB) approach to capital adequacy for credit risk plays an important role in protecting the Australian banking sector against insolvency. We outline the mathematical foundations of regulatory capital for credit risk, and extend the model specification of the IRB approach to a more ...
Typically, operational risk losses are reported above some threshold. This paper studies the impact of ignoring data truncation on the 0.999 quantile of the annual loss distribution for operational risk for a broad range of distribution parameters and truncation levels.
Risk management is an important practice in the banking industry. In this paper we develop a new methodology to estimate and predict the probability of default (PD) based on the rating transition matrices, which relates the rating transition matrices to the macroeconomic variables.
In this paper we propose a look at the capital risk problem inspired by deterministic, known from classical mechanics, problem of juggling. We propose capital equivalents to the Newton's laws of motion and on this basis we determine the most secure form of credit repayment with regard to maximisation of profit.
We analyze the size dependence and temporal stability of firm bankruptcy risk in the US economy by applying Zipf scaling techniques. We focus on a single risk factor-the debt-to-asset ratio R-in order to study the stability of the Zipf distribution of R over time.
The aim of this paper is to introduce a risk measure that extends the Gini-type measures of risk and variability, the Extended Gini Shortfall, by taking risk aversion into consideration. Our risk measure is coherent and catches variability, an important concept for risk management.
In this paper we consider reinsurance or risk sharing from a macroeconomic point of view. Our aim is to find socially optimal reinsurance treaties.
The dual risk model is a popular model in finance and insurance, which is often used to model the wealth process of a venture capital or high tech company. Optimal dividends have been extensively studied in the literature for a dual risk model.
This paper investigates the hedging effectiveness of a dynamic moving window OLS hedging model, formed using wavelet decomposed time-series. The wavelet transform is applied to calculate the appropriate dynamic minimum-variance hedge ratio for various hedging horizons for a number of assets.
Insurance risk arising from catastrophes such as earthquakes a component of the Minimum Capital Test for federally regulated property and casualty insurance companies. Analyzing earthquake insurance risk requires well-fitted spatio-temporal point process models.
Smart Close-out Netting aims to standardise and automate specific operational aspects of the legal and regulatory processes of close-out netting for prudentially regulated financial institutions. This article provides a review, analysis and perspective of these operational processes, their benefits for prudentially re...
We discuss how maximum entropy methods may be applied to the reconstruction of Markov processes underlying empirical time series and compare this approach to usual frequency sampling. It is shown that, at least in low dimension, there exists a subset of the space of stochastic matrices for which the MaxEnt method is m...
Motivated by the Basel 3 regulations, recent studies have considered joint forecasts of Value-at-Risk and Expected Shortfall. A large family of scoring functions can be used to evaluate forecast performance in this context.
We propose a generalization of the classical notion of the $V@R_{\lambda}$ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a new class of law invariant risk measures based on an appropriate family of accep...
We study pricing and hedging under parameter uncertainty for a class of Markov processes which we call generalized affine processes and which includes the Black-Scholes model as well as the constant elasticity of variance (CEV) model as special cases. Based on a general dynamic programming principle, we are able to li...
When investors have heterogeneous attitudes towards risk, it is reasonable to assume that each investor has a pricing kernel, and that these individual pricing kernels are aggregated to form a market pricing kernel. The various investors are then buyers or sellers depending on how their individual pricing kernels comp...
This paper shows that the CoVaR,$\Delta$-CoVaR,CoES,$\Delta$-CoES and MES systemic risk measures can be represented in terms of the univariate risk measure evaluated at a quantile determined by the copula. The result is applied to derive empirically relevant properties of these measures concerning their sensitivity to...
This paper develops a dynamic internal fraud model for operational losses in retail banking. It considers public operational losses arising from internal fraud in retail banking within a group of international banks.
We analyze the stability of financial investment networks, where financial institutions hold overlapping portfolios of assets. We consider the effect of portfolio diversification and heterogeneous investments using a random matrix dynamical model driven by portfolio rebalancing.
Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem and give examples of s...
If the probability of default parameters (PDs) fed as input into a credit portfolio model are estimated as through-the-cycle (TTC) PDs stressed market conditions have little impact on the results of the capital calculations conducted with the model. At first glance, this is totally different if the PDs are estimated a...
Geometric arbitrage theory reformulates a generic asset model possibly allowing for arbitrage by packaging all asset and their forward dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geomet...
We propose a definition of diversification as a binary relationship between financial portfolios. According to it, a convex linear combination of several risk positions with some weights is considered to be less risky than the probabilistic mixture of the same risk positions with the same weights.
The topological properties of interbank networks have been discussed widely in the literature mainly because of their relevance for systemic risk. Here we propose to use the Stochastic Block Model to investigate and perform a model selection among several possible two block organizations of the network: these include ...
The paper proposes an original methodology for constructing quantitative statistical models based on multidimensional distribution functions constructed on the basis of the insurance companies' data on inshurance policies (including policies with deductible) and claims incurred. Real data of some Russian insurance...
We introduce a generalized version of Orlicz premia, based on possibly non-convex loss functions. We show that this generalized definition covers a variety of relevant examples, such as the geometric mean and the expectiles, while at the same time retaining a number of relevant properties.
This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers liability liquidity risk (or funding liquidity) modeling, the second dimension focuses on asset liquidity risk (or market liquidity) modeling, and the t...
Predicting the bankruptcy risk of small and medium-sized enterprises (SMEs) is an important step for financial institutions when making decisions about loans. Existing studies in both finance and AI research fields, however, tend to only consider either the intra-risk or contagion risk of enterprises, ignoring their i...
We propose a new methodology based on the Marshall-Olkin (MO) copula to model cross-border systemic risk. The proposed framework estimates the impact of the systematic and idiosyncratic components on systemic risk.
What if the main data protection vulnerability is risk management? Data Protection merges three disciplines: data protection law, information security, and risk management.
The present paper provides a multi-period contagion model in the credit risk field. Our model is an extension of Davis and Lo's infectious default model.
This work explores the formation and propagation of systemic risks across traditional finance (TradFi) and decentralized finance (DeFi), offering a comparative framework that bridges these two increasingly interconnected ecosystems. We propose a conceptual model for systemic risk formation in TradFi, grounded in well-...
We model the influence of sharing large exogeneous losses to the reinsurance market by a bipartite graph. Using Pareto-tailed claims and multivariate regular variation we obtain asymptotic results for the Value-at-Risk and the Conditional Tail Expectation.
We show how to restructure the counterparty risk faced by the originator of a securitization or covered bond arising from an interest rate hedging swap assisted by a "one-way" collateral agreement. This risk emerges when the swap is negotiated between the special purpose vehicle and a third party that covers i...
The celebrated Expected Shortfall (ES) optimization formula implies that ES at a fixed probability level is the minimum of a linear real function plus a scaled mean excess function. We establish a reverse ES optimization formula, which says that a mean excess function at any fixed threshold is the maximum of an ES cur...
We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito, Delbaen, and Kupper (2006). These risk measures take into account not only the amounts but also the timing of a cash flow.
We present a general framework for a comparative theory of variability measures, with a particular focus on the recently introduced one-parameter families of inter-Expected Shortfall differences and inter-expectile differences, that are explored in detail and compared with the widely known and applied inter-quantile di...
We propose a novel framework of estimating systemic risk measures and risk allocations based on Markov chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event.
We introduce a trade strategy representation theorem for performance measurement and portable alpha in high frequency trading, by embedding a robust trading algorithm that describe portfolio manager market timing behavior, in a canonical multifactor asset pricing model. First, we present a spectral test for market tim...
We study the optimal investment-reinsurance problem in the context of equity-linked insurance products. Such products often have a capital guarantee, which can motivate insurers to purchase reinsurance.
In this paper, we consider the question of providing insurance protection against heavy tail losses, where the expectation of the loss may not even be finite. The product we study is based on a combination of traditional insurance up to some limit, and a parametric (or index-based) cover for larger losses.
We propose the star-shaped acceptability indexes as generalizations of both the approaches of Cherny and Madan (2009) and Rosazza Gianin and Sgarra (2013) in the same vein as star-shaped risk measures generalize both the classes of coherent and convex risk measures in Castagnoli et al. (2022). We characterize acceptab...
This paper introduces novel backtests for the risk measure Expected Shortfall (ES) following the testing idea of Mincer and Zarnowitz (1969). Estimating a regression framework for the ES stand-alone is infeasible, and thus, our tests are based on a joint regression for the Value at Risk and the ES, which allows for di...
A theoretical method is empirically illustrated in finding the best time to forsake a loan such that the overall credit loss is minimised. This is predicated by forecasting the future cash flows of a loan portfolio up to the contractual term, as a remedy to the inherent right-censoring of real-world `incomplete' p...
We propose to model the records of the maximum Drawdown in capital markets by means a Piecewise Deterministic Markov Process (PDMP). We derive statistical results such as the mean and variance that describes the sequence of maximum Drawdown records.
Asset correlations are an intuitive and therefore popular way to incorporate event dependence into event risk, e.g., default risk, modeling. In this paper we study the case of estimation of inter-sector asset correlations by separation of cross-sectional dimension and time dimension.
In this paper we attempt to introduce an econophysics approach to evaluate some aspects of the risks in financial markets. For this purpose, the thermodynamical methods and statistical physics results about entropy and equilibrium states in the physical systems are used.
Within the Own Risk and Solvency Assessment framework, the Solvency II directive introduces the need for insurance undertakings to have efficient tools enabling the companies to assess the continuous compliance with regulatory solvency requirements. Because of the great operational complexity resulting from each compl...
User financial default prediction plays a critical role in credit risk forecasting and management. It aims at predicting the probability that the user will fail to make the repayments in the future.
We present a method of hedging Conditional Value at Risk of a position in stock using put options. The result leads to a linear programming problem that can be solved to optimise risk hedging.
Decentralized finance (DeFi) is an integral component of the blockchain ecosystem, enabling a range of financial activities through smart-contract-based protocols. Traditional DeFi governance typically involves manual parameter adjustments by protocol teams or token holder votes, and is thus prone to human bias and fi...
This paper introduces a two-pillar cyber risk management framework to address the pervasive challenges in managing cyber risk. The first pillar, cyber risk assessment, combines insurance frequency-severity models with cybersecurity cascade models to capture the unique nature of cyber risk.
We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random variables, which is convenient in studying integrability, we work directly with random...
We study the effect of stochastic feeding costs on animal-based commodities with particular focus on aquaculture. More specifically, we use soybean futures to infer on the stochastic behaviour of salmon feed, which we assume to follow a Schwartz-2-factor model.
We examine a problem of demand for insurance indemnification, when the insured is sensitive to ambiguity and behaves according to the Maxmin-Expected Utility model of Gilboa and Schmeidler (1989), whereas the insurer is a (risk-averse or risk-neutral) Expected-Utility maximizer. We characterize optimal indemnity funct...
The autonomous vehicle motion prediction literature is reviewed. Motion prediction is the most challenging task in autonomous vehicles and self-drive cars.
The problem of multi-robot target tracking asks for actively planning the joint motion of robots to track targets. In this paper, we focus on such target tracking problems in adversarial environments, where attacks or failures may deactivate robots' sensors and communications.
Sampling-based model predictive control (MPC) can be applied to versatile robotic systems. However, the real-time control with it is a big challenge due to its unstable updates and poor convergence.
Unmanned ground vehicle obstacle crossing generally relies on two strategies: (i) applying a wheel torque for climbing and
Arm end-effector stabilization is essential for humanoid loco-manipulation tasks, yet it remains challenging due to the high degrees of freedom and inherent dynamic instability of bipedal robot structures. Previous model-based controllers achieve precise end-effector control but rely on precise dynamics modeling and e...
This paper applies the multibond graph approach for rigid multibody systems to model the dynamics of general spatial mechanisms. The commonly used quick return mechanism which comprises of revolute as well as prismatic joints has been chosen as a representative example to demonstrate the application of this technique ...
We address the problem of enabling quadrupedal robots to perform precise shooting skills in the real world using reinforcement learning. Developing algorithms to enable a legged robot to shoot a soccer ball to a given target is a challenging problem that combines robot motion control and planning into one task.
In recent years, the research of rehabilitation robot technology has become a hotspot in the field of rehabilitation medicine engineering and robotics. To assist active rehabilitation in patients with unilateral lower extremity injury, we propose a new self-service rehabilitation training method to control the injured...
Robotic manipulation and control has increased in importance in recent years. However, state of the art techniques still have limitations when required to operate in real world applications.
This study evaluates the integration of AI-powered robots in early childhood education, focusing on their impact on emotional self-regulation, engagement, and collaborative skills. A ten-week experimental design involving two groups of children assessed the robot's effectiveness through progress assessments, paren...
Humans can perform parkour by traversing obstacles in a highly dynamic fashion requiring precise eye-muscle coordination and movement. Getting robots to do the same task requires overcoming similar challenges.
Classical autonomous navigation systems can control robots in a collision-free manner, oftentimes with verifiable safety and explainability. When facing new environments, however, fine-tuning of the system parameters by an expert is typically required before the system can navigate as expected.
In the peg insertion task, human pays attention to the seam between the peg and the hole and tries to fill it continuously with visual feedback. By imitating the human behavior, we design architectures with position and orientation estimators based on the seam representation for pose alignment, which proves to be gene...
Robotic Manipulation (RM) is central to the advancement of autonomous robots, enabling them to interact with and manipulate objects in real-world environments. This survey focuses on RM methodologies that leverage imitation learning, a powerful technique that allows robots to learn complex manipulation skills by mimic...
We present a programming model and typing discipline for complex multi-robot coordination programming. Our model encompasses both synchronisation through message passing and continuous-time dynamic motion primitives in physical space.
Reinforcement learning (RL) algorithms hold the promise of enabling autonomous skill acquisition for robotic systems. However, in practice, real-world robotic RL typically requires time consuming data collection and frequent human intervention to reset the environment.
We present a mesoscale finger-mounted 4-degree-of-freedom (DoF) haptic device that is created using origami fabrication techniques. The 4-DoF device is a parallel kinematic mechanism capable of delivering normal, shear, and torsional haptic feedback to the fingertip.
In this paper, we investigate a predictive approach for collision risk assessment in autonomous and assisted driving. A deep predictive model is trained to anticipate imminent accidents from traditional video streams.
Multi-step cloth manipulation is a challenging problem for robots due to the high-dimensional state spaces and the dynamics of cloth. Despite recent significant advances in end-to-end imitation learning for multi-step cloth manipulation skills, these methods fail to generalize to unseen tasks.
Autonomous feeding is challenging because it requires manipulation of food items with various compliance, sizes, and shapes. To understand how humans manipulate food items during feeding and to explore ways to adapt their strategies to robots, we collected a rich dataset of human trajectories by asking them to pick up...

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