粘性解框架下的完全耦合正倒向随机系统最优控制问题的验证定理

A Verification Theorem for Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equations within the Framework of Viscosity Solutions

研究了完全耦合正倒向随机控制系统的最优控制问题.得到了粘性解框架下的,控制变量同时出现在正倒向随机系统的漂移项和扩散项中的最优控制问题的验证定理.还讨论了验证定理在构造随机最优反馈控制中的应用.

The optimal control of a fully coupled forward-backward stochastic differential equations is considered where control variables are allowed to enter into both drift and diffusion terms. A verification theorem is proved within the framework of viscosity solutions. The application of this verification theorem to the optimal stochastic feedback controls is also discussed.