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

TL;DR

This paper develops necessary and sufficient optimality conditions for stochastic control problems governed by nonlinear backward stochastic differential equations, addressing both strict and relaxed control models.

Contribution

It introduces a unified framework for deriving maximum principles applicable to both strict and relaxed controls in backward stochastic systems.

Findings

Established necessary and sufficient maximum principles for strict controls.

Extended maximum principles to relaxed controls as measure-valued processes.

Applicable to nonlinear backward stochastic differential equations.

Abstract

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.