New approach to optimal control of stochastic Volterra integral equations

TL;DR

This paper develops a new optimal control framework for stochastic Volterra integral equations with jumps, utilizing Hida-Malliavin calculus to establish existence, uniqueness, and optimality conditions, and applies it to an optimal consumption problem.

Contribution

It introduces a novel approach combining Hida-Malliavin calculus with optimal control of SVIEs with jumps, including new existence, uniqueness, and maximum principle results.

Findings

Established conditions for unique solutions of SVIEs with jumps.

Proved a sufficient maximum principle and a necessary maximum principle.

Solved an optimal consumption problem modeled by an SVIE.

Abstract

We study optimal control of stochastic Volterra integral equations (SVIE) with jumps by using Hida-Malliavin calculus. - We give conditions under which there exists unique solutions of such equations. - Then we prove both a sufficient maximum principle (a verification theorem) and a necessary maximum principle via Hida-Malliavin calculus. - As an application we solve a problem of optimal consumption from a cash flow modelled by an SVIE.