Maximum principle for delayed Volterra jumps systems using anticipating adjoints

Abstract

We establish a complete stochastic maximum principle for optimal control of stochastic Volterra integral equations with delay, Lévy processes, and partial observation. Anticipated backward stochastic Volterra integral equations characterize the adjoint processes. We rigorously establish existence and uniqueness of solutions. Employing Hida-Malliavin calculus, we derive necessary and sufficient optimality conditions. Applicability is demonstrated through explicit solutions to linear problems with memory and delay effects.