New approach to optimal control of stochastic Volterra integral equations

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.