Infinite horizon optimal control of forward-backward stochastic Volterra equations with delay

Abstract

This paper investigates an infinite-horizon optimal control problem for systems governed by coupled delayed forward-backward stochastic Volterra integral equations driven by Brownian motion and jump processes. Under partial information, we establish both necessary and sufficient stochastic maximum principles by combining localization arguments with Hida--Malliavin calculus techniques adapted to Volterra memory effects. We also study the associated infinite-horizon backward stochastic Volterra equations and prove existence and uniqueness in weighted spaces by means of a contraction mapping argument, introducing a free parameter ψ(t) which is an F∞-measurable stochastic process as in. The obtained framework extends delayed stochastic control systems with memory and provides a rigorous basis for long-term optimization problems.