Optimal Control and Nonzero-Sum Game of Stochastic Differential System and Application to Finance Market

摘要

This paper discusses the problem of optimal control and nonzero-sum game for stochastic differential system with Lévy noise and Markovian switching parameters. Based on Bellman’s principle of dynamic programming and Dynkin’s formula, a generalized Hamiltonian-Jacobi-Bellman (HJB) equation is given for solving stochastic differential games. Specifically, for a linear quadratic Gaussian nonzero-sum game with Lévy noise and Markovian switching parameters, the Nash equilibrium strategy is obtained by using this generalized HJB equation. Finally, an example of stock investment strategy optimization in financial market game is provided as an application.