On the policy improvement algorithm for ergodic risk-sensitive control

TL;DR

This paper proves the convergence of the policy improvement algorithm for ergodic risk-sensitive control problems involving multidimensional diffusions, under certain stability and cost assumptions, and explores the algorithm's region of attraction.

Contribution

It establishes the convergence of the policy improvement algorithm for a broad class of ergodic risk-sensitive control models with new stability and cost conditions.

Findings

Convergence of the policy improvement algorithm is proven for these control problems.

The region of attraction of the algorithm's equilibrium is characterized.

Results apply to multidimensional controlled diffusions on the whole space.

Abstract

In this article we consider the ergodic risk-sensitive control problem for a large class of multidimensional controlled diffusions on the whole space. We study the minimization and maximization problems under either a blanket stability hypothesis, or a near-monotone assumption on the running cost. We establish the convergence of the policy improvement algorithm for these models. We also present a more general result concerning the region of attraction of the equilibrium of the algorithm.