2017•IFAC-PapersOnLineOpen access

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

Liuwei Zhou, Wuneng Zhou, Jun Zhou, Liu Xiuqin

Abstract

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.

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Available abstract

Key concepts: Hamilton–Jacobi–Bellman equation, Differential game, Stochastic control, Mathematical economics, Stochastic differential equation, Dynamic programming, Mathematics, Nash equilibrium