Stochastic Maximum Principle for Delayed Backward Doubly Relaxed Stochastic Control Problem and Applications

摘要

we consider a measure-valued processes called relaxed controls in which an optimal solution exists, for the time delayed backward doubly stochastic differential control systems. By using the classical variational technique, a stochastic maximum principle can be deduced and it is a necessary condition of the optimal control when the set of relaxed controls is convex. In the meantime, under certain assumption, an optimality sufficient condition is gained through duality method. In the last part, our theoretical results, optimal necessary and sufficient conditions for relaxed control applied to time delayed doubly stochastic linear quadratic problem.