The group behavior analysis of the high-frequency traders based on Mean Field Games approach

We present an approach to describe the group behavior of the high-frequency traders in the stock market based on Mean Field Games and optimal control theory. The problem is formalized as a system of coupled PDEs: Kolmogorov–Fokker–Planck, evolving forward in time with initial condition, and Hamilton–Jacobi–Bellman, evolving backwards in time with terminal condition. Under certain assumptions, the system of PDEs can be reduced to Riccati-type ODEs. We solve the inverse problem to describe the behavior of the high-frequency traders during the Chinese stock market crisis in 2015.