Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon

Sun, Jingrui; Yong, Jiongmin; Zhang, Shuguang

ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 743-769.

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.

Classification : 93E20, 91A23, 49N10, 49N70
Mots clés : 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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