Stochastic maximum principle for delayed backward doubly stochastic control systems

Stochastic Maximum Principle for Controlled Backward Delayed System via Advanced Stochastic Differential Equation

The main contributions of this paper are three old. First, our primary concern is to investigate a class of stochastic recursive delayed control problems that naturally arise with strong backgrounds but have not been well studied yet. For illustration, some concrete examples are provided here. Second, it is interesting that a new class of time-advanced stochastic differential equations (ASDEs) ...

Maximum Principle for Optimal Control of Fully Coupled Forward-backward Stochastic Differential Delayed Equations

Abstract. This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the ne...

Stochastic Maximum Principle for Hilbert Space Valued Forward-Backward Doubly SDEs with Poisson Jumps

The strict and relaxed stochastic maximum principle for optimal control problem of backward systems

We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of optimality for two models. The first concerns the strict (classical) controls. The second is an extension of the first to relaxed controls, who are a measure va...

Stochastic maximum principle for optimal control problem of backward systems with terminal condition in L

We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form of stochastic maximum principle. AMS Subject Classification. 93Exx