Infinite Horizon LQ Zero-Sum Stochastic Differential Games with Markovian Jumps

Huai-Nian Zhu, Cheng-Ke Zhang, Ning Bin

School of Economics & Commence, Guangdong University of Technology, Guangzhou, China.
School of Management, Guangdong University of Technology, Guangzhou, China.

DOI: 10.4236/am.2012.330188                

Abstract

This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear It?’s differential equation with state-dependent noise and Markovian parameter jumps. Under the assumption of stochastic stabilizability, necessary and sufficient condition for the existence of the optimal control strategies is presented by means of a system of coupled algebraic Riccati equations via using the stochastic optimal control theory. Furthermore, the stochastic H_∞ control problem for stochastic systems with Markovian jumps is discussed as an immediate application, and meanwhile, an illustrative example is presented.

Keywords

Stochastic Systems; Differential Games; Markovian Jumps; Stochastic H_∞ Control

Conflicts of Interest

The authors declare no conflicts of interest.

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