The Maximum Principle for Stochastic Control Problem with Jumps in Progressive Structure

In this paper, we introduce a new structure named “progressive structure” to deal with stochastic control problem with jumps. One example is given to show the motivation of our new structure compared with the traditional one at the beginning. And then, we obtain the maximum principle for a forward stochastic control problem by virtue of a new variation method. The control is allowed to enter both diffusion and jump terms and the control domain is convex. In the end, we apply our theoretical results to another example to illustrate the efficiency of our method.