The Global Maximum Principle for Progressive Optimal Control of Partially Observed Forward-Backward Stochastic Systems with Random Jumps

Abstract

This paper is concerned with a partially observed progressive optimal control problem of forward-backward stochastic differential equations with random jumps, where the control domain is not necessarily convex, and the control variable enters into all the coefficients. In our model, the observation equation is not only driven by a Brownian motion but also a Poisson random measure, which also has correlated noises with the state equation. The partially observed global maximum principle is proved. To show its applications, a partially observed linear quadratic progressive optimal control problem of forward-backward stochastic differential equations with random jumps is investigated by the maximum principle and stochastic filtering. State estimate feedback representation of the optimal control is given in a more explicit form by introducing some ordinary differential equations.