12月15日 史敬涛教授学术报告

发布时间:2020-12-07

报告题目：Mean-Field Linear-Quadratic Stochastic Differential Games in an Infinite Horizon

主讲人：史敬涛，山东大学数学学院教授

报告时间：2020年12月15日11:15 - 12:00

报告地点：腾讯会议576672923

主持：黄永辉副教授

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).