Maximum principle for optimal control of infinite horizon stochastic difference equations driven by fractional noises

TL;DR

This paper develops a stochastic maximum principle for infinite horizon control problems driven by fractional noises, addressing the challenges posed by fractional noises on an infinite time scale, and applies it to an optimal investment scenario.

Contribution

It introduces a novel maximum principle for infinite horizon stochastic difference equations with fractional noises, extending control theory to fractional stochastic systems.

Findings

Established a maximum principle for fractional noise-driven systems

Solved an optimal investment problem using the developed theory

Addressed the challenge of fractional noises on infinite horizons

Abstract

In this paper, infinite horizon stochastic difference equations and backward stochastic difference equations with fractional noises are studied. The main difficulty comes from fractional noises on infinite horizon. Motivated by discrete-time optimal control problem driven by fractional noises and on infinite horizon, the stochastic maximum principle for discrete-time control problem driven by fractional noises in infinite horizon is proved. As an application, an optimal investment problem is solved.