Infinite Horizon Optimal Control of Forward-Backward Stochastic Volterra Equations with Delay

TL;DR

This paper develops maximum principles for infinite horizon control of systems described by coupled forward-backward stochastic Volterra equations with delay, using advanced calculus techniques.

Contribution

It introduces new maximum principles and proves existence and uniqueness results for infinite horizon backward stochastic Volterra integral equations.

Findings

Established sufficient and necessary maximum principles.

Proved existence and uniqueness for a class of infinite horizon BSVIEs.

Applied Hida-Malliavin calculus to stochastic Volterra systems.

Abstract

We consider an optimal control problem for infinite horizon systems governed by coupled forward-backward stochastic Volterra integral equations with delay. Using Hida-Malliavin calculus, we prove both sufficient and necessary maximum principles for optimal control of such systems. We establish existence and uniqueness results for a class of infinite horizon backward stochastic Volterra integral equations (BSVIEs).