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Sun, Jingrui; Yong, Jiongmin; Zhang, Shuguang

Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon. (English) Zbl 1342.93122

ESAIM, Control Optim. Calc. Var. 22, No. 3, 743-769 (2016).
Summary: This paper is concerned with a linear quadratic stochastic two-person zero-sum differential game with constant coefficients in an infinite time horizon. Open-loop and closed-loop saddle points are introduced. The existence of closed-loop saddle points is characterized by the solvability of an algebraic Riccati equation with a certain stabilizing condition. A crucial result makes our approach work is the unique solvability of a class of linear backward stochastic differential equations in an infinite horizon.

Cited in 11 Documents

MSC:

93E20 Optimal stochastic control
91A23 Differential games (aspects of game theory)
49N10 Linear-quadratic optimal control problems
49N70 Differential games and control

Keywords:

linear quadratic stochastic differential game; two-person; zero-sum; infinite horizon; open-loop and closed-loop saddle points; algebraic Riccati equation; stabilizing solution
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References:

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