This paper considers the fully coupled forward-backward stochastic functional differential equations (FBSFDEs) with stochastic functional differential equations as the forward equations and the generalized anticipated backward stochastic differential equations as the backward equations. The authors will prove the existence and uniqueness theorem for FBSFDEs. As an application, we deal with a quadratic optimal control problem for functional stochastic systems, and get the explicit form of the optimal control by virtue of FBSFDEs.

中文翻译：

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完全耦合的正向-后向随机函数微分方程及其在二次最优控制中的应用

本文将具有随机泛函的微分方程组（FBSFDEs）与随机泛函微分方程组作为正向方程组，将广义预期的反向随机泛函微分方程组视为反向方程组。作者将证明FBSFDE的存在性和唯一性定理。作为应用，我们处理了功能随机系统的二次最优控制问题，并借助FBSFDE得到了最优控制的显式形式。