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.

DOI: 10.1051/cocv/2015024

Keywords: Linear quadratic stochastic differential game, two-person, zero-sum, infinite horizon, open-loop and closed-loop saddle points, algebraic Riccati equation, stabilizing solution

^{1}; Yong, Jiongmin

^{2}; Zhang, Shuguang

^{3}

@article{COCV_2016__22_3_743_0, 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://archive.numdam.org/articles/10.1051/cocv/2015024/} }

TY - JOUR AU - Sun, Jingrui AU - Yong, Jiongmin AU - Zhang, Shuguang TI - Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 743 EP - 769 VL - 22 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2015024/ DO - 10.1051/cocv/2015024 LA - en ID - COCV_2016__22_3_743_0 ER -

%0 Journal Article %A Sun, Jingrui %A Yong, Jiongmin %A Zhang, Shuguang %T Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 743-769 %V 22 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2015024/ %R 10.1051/cocv/2015024 %G en %F COCV_2016__22_3_743_0

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, Volume 22 (2016) no. 3, pp. 743-769. doi : 10.1051/cocv/2015024. http://archive.numdam.org/articles/10.1051/cocv/2015024/

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