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Evaluation |
Inherit to new Generation after Crossover and Mutation |
Repeat Ne generations |
Fig. 1: My model |
2 Model |
in the artificial market simulation. The genetic algo- |
rithmsearchthegenemostearnsprofit. Thissearching |
A human building an AI trader (builder) gives the correspondswithwhattheAItraderlearnshowtrades |
AI trader candidates of trading strategies, and makes earns profit. |
theAItradertolearnwhichstrategiesandparameters Of course, trades of the AIA impact market prices |
earn more. This study focuses whether an AI trader intheartificialmarket,butforthepurposeofcompar- |
candiscovermarketmanipulationthroughlearningde- ison, I also investigated the case without the impacts |
spitethebuilderhasnointentionofmarketmanipula- to market prices (backtesting). |
tion2. In the following, at first I explain the artificial mar- |
Fig. 1schematicallyshowsamodelofthisstudy. An ketsimulationevaluatingeachgeneandthen,Iexplain |
AI trader that the builder intents no trading strategy the genetic algorithm searching the gene most earns |
is modeled using a genetic algorithm in which a gene profit. |
includesalltrades. Eachgeneisevaluatedintheartifi- |
cial market simulation. The artificial market includes |
2.1 Artificial Market Simulation |
an AI agent (AIA) that trades exactly same as one |
geneindicating. ThegeneisevaluatedbyAIA’sprofit In this study, I built an artificial market model added |
an AIA to the artificial market model of Mizuta [2] |
2In reality, the builder always intents some kinds of strate- In the model here, there is one stock. The stock |
gies in the process of picking up and modeling candidates of exchange adopts a continuous double auction to de- |
strategies. In contrast, it is very important for this study that |
termine the market price. In this auction mechanism, |
the builder has no intention of any strategies including market |
multiple buyers and sellers compete to buy and sell |
manipulation. Therefore, I do not intentionally modeled trad- |
ing strategies and my model directly searches for all the best financial assets in the market, and transactions can |
trades in an artificial market environment. Due to no models occur at any time whenever an offer to buy and an of- |
oftradingstrategiesmymodelcannotmakeanyoutputsinan |
fertosellmatch. Theminimumunitofpricechangeis |
out-sample,thennoonecantestmymodelinanout-sample. I |
argue,however,thatthisstudyneedsnoevaluationsinanout- δP. The buy-order price is rounded off to the nearest |
samplebecausethisstudyfocuseswhetheranAItradercandis- fraction, and the sell-order price is rounded up to the |
covermarketmanipulationthroughlearningdespitethebuilder nearest fraction. |
has no intention of market manipulation. This study does not |
The model includes n normal agents (NAs) and an |
aimtousemymodelinactualfinancialmarketsthatareinan |
out-sampleenvironment. AIA.Agentscanshortsellfreely. Thequantityofhold- |
2 |
ing positions is not limited, so agents can take any whenPt >Pt ,theNAplacesanordertobuyone |
e,j o,j |
shares for both long and short positions to infinity. share, but |
Agents always places an order for only one share. I whenPt <Pt ,theNAplacesanordertosellone |
e,j o,j |
employed “tick time” t that increase by one when an share4. The remaining order is canceled after t from |
c |
agent orders. the order time. |
2.1.1 Normal Agent (NA) |
2.1.2 AI Agent (AIA) |
To replicate the nature of price formation in actual |
Every δt tick time the AIA takes one of three actions |
financialmarkets,IintroducedtheNAtomodelavery |
that are buy one share (at the lowest sell order price |
general investor. The number of NAs is n. First, at |
on the order book), sell one share (at the highest buy |
time t = 1, NA No. 1 places an order to buy or sell |
order price on the order book) and no action5. The |
its risk asset; then, at t = 2,3,,,n, NAs No. 2,3,,,n |
AIA takes actions N = (t − t )/δt times through |
respectively place buy or sell orders. At t=n+1, the t e c |
the whole one artificial market simulation, where one |
model returns to the first NA and repeats this cycle. |
simulation runs until tick time t . The actions are |
An NA determines an order price and buys or sells as e |
givenbyonegeneinthegeneticalgorithmasfollowing |
follows. It uses a combination of a fundamental value |
I will mention. |
and technical rules to form an expectation on a risk |
asset’sreturn. Theexpectedreturnofagentj foreach |
risk asset is 2.2 Genetic Algorithm |
P Pt−1 |
rt =(w log f +w log +w (cid:15)t)/Σ3w 2.2.1 Genes and Artificial Market |
e,j 1,j Pt−1 2,j Pt−τj−1 3,j j i i,j |
(1) Fig. 1 schematically shows a model of this study. An |
where w i,j is the weight of term i for agent j and is AI trader that the builder intents no trading strategy |
independently determined by random variables uni- is modeled using a genetic algorithm. The number of |
formly distributed on the interval (0,w i,max) at the genes is N g. One gene has information of actions and |
start of the simulation for each agent. log is natural the number of actions that one gene has is N . Each |
t |
logarithm. P f is a fundamental value and is a con- action is one of three actions that are buy one share, |
stant. Pt is a market price that is the mid price (the sell one share and no action. Each gene is evaluated |
average price of the highest buy order price and the by profit of the AIA in an artificial market, in where |
lowest sell order price), and (cid:15)t j is determined by ran- the AIA trades every δt tick time same as N t actions |
domvariablesfromanormaldistributionwithaverage one gene indicating. When the AIA holds stocks at |
0 and variance σ (cid:15). Finally, τ j is independently deter- the end of a simulation, the stocks are evaluated as |
mined by random variables uniformly distributed on P . All artificial markets has exactly same NAs using |
f |
the interval (1,τ max) at the start of the simulation for same random numbers. Therefore, if the AIA trades |
each agent3. same,theartificialmarketsoutputsamemarketprices |
The first term of Eq. (1) represents a fundamental and same NAs’ trades. |
strategy: the NA expects a positive return when the |
market price is lower than the fundamental value, and |
vice versa. The second term of Eq. (1) represents a 2.2.2 Inheritance to Next Generation |
technical strategy using a historical return: the NA |
The top N genes that earned most are not changed |
expects a positive return when the historical market ge |
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