学术报告(史敬涛 12.15)

Mean-Field Linear-Quadratic Stochastic Differential Games in an Infinite Horizon

发布人:杨晓静 发布日期:2020-12-10
主题
Mean-Field Linear-Quadratic Stochastic Differential Games in an Infinite Horizon
活动时间
-
活动地址
腾讯会议, 收听账号及密码:576672923
主讲人
史敬涛教授 山东大学必赢唯一官方网站
主持人
黄永辉

摘要:

This talk is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. Existence of an open-loop Nash equilibrium is characterized by the solvability of a system of mean-field forward-backward stochastic differential equations in an infinite horizon and the convexity of the cost functionals, and the closed-loop representation of an open-loop Nash equilibrium is given through the solution to a system of two coupled non-symmetric algebraic Riccati equations. The existence of a closed-loop Nash equilibrium is characterized by the solvability of a system of two coupled symmetric algebraic Riccati equations. Two-person mean-field linear-quadratic zero-sum stochastic differential games in an infinite time horizon are also considered. Both the existence of open-loop and closed-loop saddle points are characterized by the solvability of a system of two coupled generalized algebraic Riccati equations with static stabilizing solutions. Mean-field linear-quadratic stochastic optimal control problems in an infinite horizon are discussed as well, for which it is proved that the open-loop solvability and closed-loop solvability are equivalent.

 

Joint work with Professor Xun Li (PolyU) and Professor Jiongmin Yong (UCF).