A General Maximum Principle for Progressive Optimal Control of Fully Coupled Forward-Backward Stochastic Systems with Jumps

Abstract: This paper is concerned with a general maximum principle for the fully coupled forward-backward stochastic optimal control problem with jumps, where the control domain is not necessarily convex, within the progressively measurable framework. A distinct feature in this paper is that the solution $Z$ of BSDEPs could include the variable ``$e$'', further, the diffusion term of BSDEPs takes the form $\int_{\mathcal{E}}Z_{(t,e)}\nu(d e)d W_t$ rather than the conventional $Z_t dW_t$, reflecting the essential coupling between the solution component $Z$ and the Polish space $\mathcal{E}$.