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.

中文翻译：

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前-后向随机差分系统随机最优控制问题的极大原理

在本文中，我们研究了正反向随机差分系统（FBSΔSs）的随机最优控制问题的极大原理。研究了两种类型的 FBSΔS。第一个由部分耦合的前向后随机差分方程（FBSΔE）描述，第二个由完全耦合的 FBSΔE 描述。通过对乘积规则的适当表示和伴随过程的适当表述，我们推导出伴随差分方程。最后，建立了控制域为凸的最优控制问题的最大原理。