LINEAR QUADRATIC ZERO-SUM STOCHASTIC DIFFERENTIAL GAMES WITH MARKOV REGIME SWITCHING
ZHU Huainian, ZHI Jinghan ,ZHANG Chengke , BIN Ning
Author information+
School of Management, Guangdong University of Technology, Guangzhou 510520; School of Economics and Commence, Guangdong University of Technology, Guangzhou 510520
In this paper, we discuss the problem of a class of linear quadratic zero-sum stochastic differential games with Markov regime switching in continuous time. Under the condition of generalized It\^{o}'s differential rule, by introducing a generalized Riccati differential (algebraic) equation, it is proved that the solvability of the associated generalized Riccati equation is both sufficient and necessary condition for the existence of equilibrium strategies, meanwhile, the explicit solution of equilibrium strategies with closed form and the optimal value of cost functional are obtained. Fi ally, a numerical example is given to illustrate the validity of the obtained results.
LINEAR QUADRATIC ZERO-SUM STOCHASTIC DIFFERENTIAL GAMES WITH MARKOV REGIME SWITCHING. Journal of Systems Science and Mathematical Sciences, 2013, 33(12): 1391-1403 https://doi.org/10.12341/jssms12215