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

TL;DR

This paper establishes a comprehensive maximum principle for optimal control problems involving fully coupled forward-backward stochastic systems with jumps, accommodating non-convex control domains and complex solution structures.

Contribution

It introduces a novel maximum principle framework for fully coupled forward-backward stochastic systems with jumps, including new solution features and coupling mechanisms.

Findings

Derived a maximum principle for non-convex control domains.

Included the variable 'e' in the solution Z of BSDEPs.

Modeled the diffusion term with integral over space , capturing coupling.

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 $\mathcal{E}$.