LQ stochastic optimal control of forward-backward stochastic control system driven by Lévy process

Abstract

This work analyzes one kind of linear quadratic (LQ) stochastic control problem. The controlled system in this paper is described by a linear FBSDE driven by Levy process. We prove the existence and uniqueness of the explicit control for this control system, and finally get the explicit form of the optimal control by one kind of generalized Riccai equation. In the end, we give a simple control system as an example.