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

TL;DR

This paper develops a stochastic maximum principle for optimal control problems involving nonlinear backward stochastic differential equations with L1 terminal conditions, providing necessary conditions for optimality.

Contribution

It introduces a novel maximum principle for backward systems with L1 terminal data, expanding the theoretical framework for stochastic control.

Findings

Derived necessary optimality conditions for the control problem.

Extended maximum principle to systems with L1 terminal conditions.

Applicable to nonlinear backward stochastic differential equations.

Abstract

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.