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
Sun, Jingrui 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 = {https://www.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 - https://www.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 https://www.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
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