Linear Quadratic Stochastic Two-Person Zero-Sum Differential Games in an Infinite Horizon

摘要

This paper is concerned with a linear quadratic stochastic two-personzero-sum differential game with constant coefficients in an infinite timehorizon. Open-loop and closed-loop saddle points are introduced. The existenceof closed-loop saddle points is characterized by the solvability of analgebraic Riccati equation with a certain stabilizing condition. A crucialresult makes our approach work is the unique solvability of a class of linearbackward stochastic differential equations in an infinite horizon.