Optimal control of forward-backward stochastic Volterra equations

TL;DR

This paper develops a maximum principle for controlling coupled forward-backward stochastic Volterra equations, providing existence, uniqueness results, and applying the theory to a recursive utility optimization problem in finance with memory effects.

Contribution

It introduces a novel maximum principle for coupled stochastic Volterra systems using Hida-Malliavin calculus, and demonstrates its application to financial utility optimization.

Findings

Established existence and uniqueness of solutions for backward stochastic Volterra equations.

Derived necessary and sufficient maximum principles for optimal control.

Applied the theoretical framework to a recursive utility optimization in finance.

Abstract

We study the problem of optimal control of a coupled system of forward-backward stochastic Volterra equations. We use Hida-Malliavin calculus to prove a sufficient and a necessary maximum principle for the optimal control of such systems. Existence and uniqueness of backward stochastic Volterra integral equations are proved. As an application of our methods, we solve a recursive utility optimisation problem in a financial model with memory.