A maximum principle for fractional diffusion processes with infinite horizon

TL;DR

This paper establishes a maximum principle for optimal control of fractional diffusion processes over an infinite horizon and demonstrates the existence of related fractional backward stochastic differential equations, supported by an example.

Contribution

It introduces a maximum principle for fractional diffusion control problems with infinite horizon and proves the existence of fractional backward stochastic differential equations in this setting.

Findings

Maximum principle for fractional diffusion control with infinite horizon

Existence of fractional backward stochastic differential equations on infinite horizon

Illustrative example demonstrating the theoretical results

Abstract

We prove a maximum principle for the problem of optimal control for a fractional diffusion with infinite horizon. Further, we show existence of fractional backward stochastic differential equations on infinite horizon. We illustrate our findings with an example.