A Necessary Condition for Optimal Control of Forward-Backward Stochastic Control System with Levy Process in Nonconvex Control Domain Case

This paper analyzes one kind of optimal control problem which is described by forward-backward stochastic differential equations with Levy process (FBSDEL). We derive a necessary condition for the existence of the optimal control by means of spike variational technique, while the control domain is not necessarily convex. Simultaneously, we also get the maximum principle for this control system when there are some initial and terminal state constraints. Finally, a financial example is discussed to illustrate the application of our result.