勷勤数学•专家报告

题      目：Stochastic Differential Games with Random Coefficients and Stochastic Hamilton-Jacobi-Bellman-Isaacs Equations

报  告  人：张静    副教授  (邀请人：杨舟)

                                   复旦大学

时      间：7月18日  15：00-16：00

地     点：西楼二楼会议室

报告人简介:

       张静，2012年于法国埃夫里大学获理学博士学位，现为复旦大学数学科学学院运筹学与控制论方向副教授。主要研究方向：随机偏微分方程，随机控制等，在《Ann. Probab.》、《 Electron. J. Probab.》、《 Stoch. Dyn.》等杂志发表多篇论文。

摘      要：

       We study a class of zero-sum two-player stochastic differential games with the controlled stochastic differential equations and the payoff/cost functionals of recursive type. As opposed to the pioneering work by Fleming and Souganidis [Indiana Univ. Math. J., 1989] and the seminal work by Buckdahn and Li [SIAM J. Control Optim., 2008], the involved coefficients may be random, going beyond the Markovian framework and leading to the random upper and lower value functions. We first prove the dynamic programming principle for the game, and then under the standard Lipschitz continuity assumptions on the coefficients, the upper and lower value functions are shown to be the viscosity solutions of the upper and the lower fully nonlinear stochastic Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations, respectively.  A stability property of viscosity solutions is also proved. Under certain additional regularity assumptions on the diffusion coefficient, the uniqueness of the viscosity solution is addressed as well.

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