New approach to optimal control of delayed stochastic Volterra integral equations

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.

This work is now in its final form. It only remains to further develop the introduction in order to incorporate some results that have recently been brought to our attention