New approach to optimal control of delayed stochastic Volterra integral equations

TL;DR

This paper develops a new theoretical framework using Hida-Malliavin calculus to derive maximum principles for optimal control of delayed stochastic Volterra integral equations.

Contribution

It introduces a novel approach linking adjoint processes to anticipated backward stochastic Volterra integral equations for delayed stochastic systems.

Findings

Derived necessary and sufficient maximum principles for control.

Established the structure of adjoint processes via ABSVIE.

Provided a rigorous framework for delayed stochastic control.

Abstract

We address the optimal control of stochastic Volterra integral equations with delay through the lens of Hida-Malliavin calculus. We show that the corresponding adjoint processes satisfy an anticipated backward stochastic Volterra integral equation (ABSVIE), and, exploiting this structure, we establish both necessary and sufficient stochastic maximum principles. Our results provide a comprehensive and rigorous framework for characterizing optimal controls in delayed stochastic systems.