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