报告时间：2017年5月4日（星期四）上午10:20-11:20

报告地点：知新楼B座1238

报告人：孟庆欣，湖州师范大学

报告题目：Stochastic Hamilton-Jacobi-Bellman equations with jumps

报告摘要：This paper is mainlyconcerned withastochastic HJB equation with Poisson jumps which is a fully nonlinear backward stochastic partial differential equation.It is motivatedby astochastic optimal problem where the controlled systems are drivenby Brownian motion and Poisson jumps with random coefficients. Firstly we establish the dynamic programming principle for the corresponding stochastic optimal control problem to derive the general form of stochastic HJB equation with jumps. Secondly, we establish an verification theory which can construct an optimal pairfor the optimal control problem. At last, we prove the existence and uniqueness result for some special form of stochastic HJB equation with jumps inthe sense of Sobolev space. To this end, the most important step isthat we must first establish the existence and uniqueness result fora class of backward stochastic evolution equations with jumps inHilbert spaces. Then we recast the stochastic HJB equation withjumps as the backward stochastic evolution equation with jumps inHilbert spaces to the existence and uniqueness results.