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 valued processes

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 as well as sufficient conditions of optimality, in the form of global stochastic maximum principle, for two models. The first concerns the relaxed controls, who are a measure-valued processes. The second is a restriction of the first to strict control problems.Comment: 33 page

Stochastic maximum principle for optimal control problem of backward systems with terminal condition in L1

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

Necessary and sufficient optimality conditions for relaxed and strict control problems of backward systems

We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we establish necessary as well as sufficient conditions of optimality for two models. The first concerns the relaxed controls, who are measure-valued processes. The second is a particular case of the first and relates to strict control problems

mixed relaxed-singular control problems

general stochastic maximum principle fo

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general necessary and sufficient optimality conditions for singular control problem