Risk-sensitive control of reflected diffusion processes on orthrant

TL;DR

This paper establishes the existence of optimal risk-sensitive controls for reflected diffusion processes within orthants, using a near monotone condition on the running cost.

Contribution

It introduces a novel approach to prove the existence of optimal risk-sensitive controls under state constraints with a near monotone cost assumption.

Findings

Existence of optimal risk-sensitive control proven.

Applicable to reflected diffusion processes on orthants.

Uses near monotone assumption on running cost.

Abstract

In this article, we prove the existence of optimal risk-sensitive control with state constraints. We use near monotone assumption on the running cost to prove the existence of optimal risk-sensitive control.