发表机构
University of Biskra; Brandenburg University of Technology Cottbus–Senftenberg（比斯克拉大学; 科特布斯-森夫滕堡勃兰登堡工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对带反射约束的解耦FBSDE随机最优控制问题，提出变分方法，通过惩罚和残差项分离推导出Pontryagin型反射变分不等式，给出必要最优性条件。
AI 中文摘要
本文研究了由解耦正倒向随机微分方程（FBSDE）控制的随机控制问题的必要最优性条件，其中倒向分量带有反射约束。代价泛函通过反射BSDE的初值定义，其下障碍依赖于前向状态。反射项的非光滑性质阻碍了经典变分方法的直接应用。利用惩罚方法、尖峰变分和对偶论证，我们推导出一个惩罚变分关系。我们方法的一个关键特征是将反射贡献分离为一个残差项，从而避免对非光滑惩罚算子进行微分，同时保留类似于经典随机最大值原理的哈密顿伴随结构。通过取极限，我们得到了Pontryagin型的反射变分不等式，其中障碍效应通过与反射项相关的残差贡献被显式表示。
英文摘要
This paper studies necessary optimality conditions for stochastic control problems governed by decoupled forward--backward stochastic differential equations with reflection constraints on the backward component. The cost functional is defined through the initial value of a reflected BSDE whose lower obstacle depends on the forward state. The nonsmooth nature of the reflection term prevents the direct application of classical variational methods. Using a penalization approach, spike variations, and duality arguments, we derive a penalized variational relation. A key feature of our method is to isolate the reflection contribution into a residual term, avoiding the differentiation of the nonsmooth penalization operator while preserving a Hamiltonian adjoint structure analogous to the classical stochastic maximum principle. Passing to the limit yields a reflected variational inequality of Pontryagin type, where the obstacle effect is explicitly represented through a residual contribution associated with the reflection term.
