标题：Controlled Mean-Field Backward Stochastic Differential Equations with Jumps Involving the Value Function
作者：Li Juan; Min Hui
作者机构：[Li, J] School of Mathematics and Statistics, Shandong University, Weihai, Weihai, 264209, China;[ Min, H] School of Mathematics and Statistics, Shand 更多
通讯作者地址：[Min, H]Shandong Univ, Sch Math & Stat, Weihai 264209, Weihai, Peoples R China.
关键词：Dynamic programming principle (DPP);Hamilton-Jacobi-Bellman (HJB) equation;mean-field backward stochastic differential equation (mean-field BSDE) with jump;Poisson random measure;value function
摘要：This paper discusses mean-field backward stochastic differential equations (mean-field BSDEs) with jumps and a new type of controlled mean-field BSDEs with jumps, namely mean-field BSDEs with jumps strongly coupled with the value function of the associated control problem. The authors first prove the existence and the uniqueness as well as a comparison theorem for the above two types of BSDEs. For this the authors use an approximation method. Then, with the help of the notion of stochastic backward semigroups introduced by Peng in 1997, the authors get the dynamic programming principle (DPP) for the value functions. Furthermore, the authors prove that the value function is a viscosity solution of the associated nonlocal Hamilton-Jacobi-Bellman (HJB) integro-partial differential equation, which is unique in an adequate space of continuous functions introduced by Barles, et al. in 1997.