The Maximum Principle for progressive optimal ctochastic control problems with random jumps
[TMCSC]
July 20, 2021 15:00-16:00
地点：四川大学数学学院东409
![[lecture]吴臻0714-01.png](http://tianyuan.scu.edu.cn/upload/default/20210714/%5Blecture%5D%E5%90%B4%E8%87%BB0714-01.png "[lecture]吴臻0714-01.png")
SPEAKER
吴臻（山东大学）
ABSTRACT
In this talk, we consider a control problem driven by Brownian Motions and Poisson random measures. The control is allowed to enter both diffusion and jump terms and the control domain need not be convex. We obtain the maximum principle for optimal controls of stochastic systems with jumps by introducing a new method of variation. However, the variation of the optimal control is no longer predictable. We overcome this difficulty by introducing the stochastic integral with respect to progressive integrand and allowing all admissible controls to be progressive instead of predictable. When the control domain is convex and controls are progressive, we give two necessary conditions that the optimal control satisfies. One condition is a characterization of the optimal control in “continuous” times, and the other condition is a characterization of the optimal control in “jump” times.
ORGANIZERS
陈柏辉（四川大学）
李洪旭（四川大学）
寇 辉（四川大学）
连 增（四川大学）
SUPPORTED BY
国家天元数学西南中心
四川大学数学学院