An optimal control problem of forward-backward stochastic Volterra integral equations with state constraints

TL;DR

This paper develops a stochastic maximum principle for optimal control problems involving forward-backward stochastic Volterra integral equations with state constraints, providing necessary conditions for optimal controls using variational methods.

Contribution

It introduces a new stochastic maximum principle for FBSVIEs with state constraints, expanding the theoretical framework for such control problems.

Findings

Derived a variational inequality using Ekeland's principle

Established a stochastic maximum principle for FBSVIEs

Provided necessary conditions for optimal controls in constrained systems

Abstract

This paper is devoted to the stochastic optimal control problems for systems governed by forward-backward stochastic Volterra integral equations (FBSVIEs, for short) with state constraints. Using Ekeland's variational principle, we obtain one kind of variational inequality. Then, by dual method, we derive a stochastic maximum principle which gives the necessary conditions for the optimal controls.