Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon∗
School of Mathematical Sciences, University of Science and
Technology of China, Hefei, Anhui
230026, P.R. of
2 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA.
3 Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China.
Revised: 28 March 2015
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.
Mathematics Subject Classification: 93E20 / 91A23 / 49N10 / 49N70
Key words: 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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