勷勤数学•专家报告

题      目：Infinite time horizon stochastic recursive control problems with jumps: dynamic programming and stochastic verification theorems

报  告  人： 魏庆萌 教授  (邀请人：杨舟)

                                     东北师范大学

时      间： 1月27日  16：00-17:00

地     点：数科院西楼二楼会议室

报告人简介:

        魏庆萌，2013年博士毕业于山东大学，现为东北师范大学教授、博士生导师，入选国家级、省级高层次人才，国家天元数学东北中心优秀青年学者等；主持国家自然科学基金面上项目、吉林省自然科学基金优秀青年基金等科研项目；获山东省自然科学奖一等奖、山东省优秀博士论文等奖励。主要从事倒向随机微分方程、随机控制及金融数学的研究工作，研究成果发表在SICON、AMO、ESAIM: COCV、SPA、Science China Mathematics等国际著名期刊。

摘      要：

        This talk is about an infinite time horizon stochastic recursive control problem with jumps, where an infinite time horizon stochastic differential equation and backward stochastic differential equation with jumps describes the state process and the cost functional, respectively. By establishing the dynamic programming principle, we relate the value function of the control problem with integral-partial differential equation of HJB type in the sense of viscosity solutions. On the other hand, stochastic verification theorems are also studied to provide sufficient conditions to verify the optimality of the given admissible controls. Such a study is carried out in the framework of classical solutions but also in that of viscosity solutions. Our work emphasizes important differences from the approach for finite time horizon problems. In particular, we have to work in an Lp-setting for p>4 in order to study the verification theorem in viscosity sense.

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