反射正倒向随机微分方程随机控制问题的随机验证定理
Stochastic Verification Theorems for Stochastic Control Problems of Reflected FBSDEs
AI总结：
本文在经典解与粘性解框架下建立反射 FBSDEs 随机控制问题的随机验证定理，给出最优性充分条件并构造反馈最优控制律，且通过两个实例加以应用。
摘要：
本文研究了反射正倒向随机微分方程（FBSDEs）随机控制问题的随机验证定理。我们在经典解与粘性解两种框架下开展工作，给出了验证控制为最优的充分条件。此外，我们还从相应的带障碍 Hamilton-Jacobi-Bellman（HJB）方程的经典解和粘性解出发，构造了反馈最优控制律。最后，我们将理论结果应用于两个具体例子：一个针对经典解情形，另一个针对粘性解情形。
英文摘要：
In this paper, the stochastic verification theorems for stochastic control problems of reflected forward-backward stochastic differential equations are studied. We carry out the work within the frameworks of classical and viscosity solutions. The sufficient conditions of verifying the controls to be optimal are given. We also construct the feedback optimal control laws from the classical and viscosity solutions of the associated Hamilton-Jacobi-Bellman equations with obstacles. Finally, we apply the theoretical results in two concrete examples. One is for the case of the classical solution, and the other is for the case of the viscosity solution.
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