| Issue |
ESAIM: COCV
Volume 22, Number 3, July-September 2016
|
|
|---|---|---|
| Page(s) | 743 - 769 | |
| DOI | https://doi.org/10.1051/cocv/2015024 | |
| Published online | 16 May 2016 | |
Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon∗
1
School of Mathematical Sciences, University of Science and
Technology of China, Hefei, Anhui
230026, P.R. of
China.
sjr@mail.ustc.edu.cn
2
Department of Mathematics, University of Central
Florida, Orlando,
FL
32816, USA.
jiongmin.yong@ucf.edu
3
Department of Statistics and Finance, University of Science and
Technology of China, Hefei, Anhui
230026, P.R.
China.
sgzhang@ustc.edu.cn
Received:
28
April
2014
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
© EDP Sciences, SMAI 2016
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