Geodesic
Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon
Sun, Jingrui1  ; Yong, Jiongmin2  ; Zhang, Shuguang3
1 School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, P.R. of China.
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.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 743-769

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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.

Reçu le :
DOI : 10.1051/cocv/2015024
Classification : 93E20, 91A23, 49N10, 49N70
Keywords: Linear quadratic stochastic differential game, two-person, zero-sum, infinite horizon, open-loop and closed-loop saddle points, algebraic Riccati equation, stabilizing solution

Sun, Jingrui 1 ; Yong, Jiongmin 2 ; Zhang, Shuguang 3

1 School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, P.R. of China.
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. 
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     author = {Sun, Jingrui and Yong, Jiongmin and Zhang, Shuguang},
     title = {Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {743--769},
     publisher = {EDP-Sciences},
     volume = {22},
     number = {3},
     year = {2016},
     doi = {10.1051/cocv/2015024},
     zbl = {1342.93122},
     mrnumber = {3527942},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015024/}
}
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Sun, Jingrui; Yong, Jiongmin; Zhang, Shuguang. Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 743-769. doi: 10.1051/cocv/2015024

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