Past

NUMERICAL STUDY INTO STOCK MARKET CRISES BASED ON MEAN FIELD GAMES APPROACH

Abstract

We present an approach to describe the stock market crises based on Mean Field Games and Optimal Control theory with a turnpike effect. The impact of the large amount of high-frequency traders (HFTs) can be modelled via mean field term. A Mean Field Game is a coupled system of PDEs: a Kolmogorov–Fokker–Planck equa-tion, evolving forward in time and describing evolution of the HFTs probability den-sity function spread by the amount of asset shares; and a Hamilton–Jacobi–Bellman equation, evolving backwards in time and defining the strategy of the HFTs. These equations form a boundary value problem