Maximum Principle for Forward-Backward Stochastic Control System Driven by Lévy Process

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...

A general stochastic maximum principle for optimal control problems of forward-backward systems

Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem impossible to solve by the classical method of spike variation. In this paper, we introduce a new approach to solve this open problem and we establish necessary ...

A Forward-backward Algorithm for Stochastic Control Problems - Using the Stochastic Maximum Principle as an Alternative to Dynamic Programming

An algorithm for solving continuous-time stochastic optimal control problems is presented. The numerical scheme is based on the stochastic maximum principle (SMP) as an alternative to the widely studied dynamic programming principle (DDP). By using the SMP, (Peng, 1990) obtained a system of coupled forwardbackward stochastic differential equations (FBSDE) with an external optimality condition. ...

Stochastic maximum principle for optimal control problem of backward system 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

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