Maximum principle for stochastic optimal control problem of forward–backward stochastic difference systems

Abstract

In this paper, we study the maximum principle for stochastic optimal control problems of forward–backward stochastic difference systems (FBSΔSs). Two types of FBSΔSs are investigated. The first one is described by a partially coupled forward–backward stochastic difference equation (FBSΔE) and the second one is described by a fully coupled FBSΔE. By adopting an appropriate representation of the product rule and an appropriate formulation of the adjoint process, we deduce the adjoint difference equation. Finally, the maximum principle for this optimal control problem with the control domain being convex is established.