Numerical study of the stock market crises based on Mean Field Games approachстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 26 января 2022 г.
Аннотация:We present an approach to describe the stock market crises based on MeanField Games (MFGs) and Optimal Control theory with a turnpike effect. The impact ofthe large amount of high-frequency traders (HFTs) can be modeled via mean field term.We introduce the turnpike as a function that relies on the changes of the asset share price.A MFG is a coupled system of PDEs: a Kolmogorov–Fokker–Planck equation, evolvingforward in time and a Hamilton–Jacobi–Bellman equation, evolving backwards in time.The ill-posedness of this system comes from a turnpike effect. The numerical solution ofan extremal problem that is dual to PDEs system is presented. We apply this approach todescribe the Chinese stock market crash in 2015 considering the representative stock ofCITIC Securities (ticker 600030). We consider HFTs that form dominating bull and bearmarket. As a result, the bull strategy imitators do not make any profit.