Ergodic Risk-Sensitive Control for Regime-Switching Diffusions

TL;DR

This paper addresses the ergodic risk-sensitive control problem for regime-switching diffusions, providing solutions to associated eigenvalue problems and characterizing optimal controls under stability assumptions.

Contribution

It introduces novel methods for solving nonlinear eigenvalue problems in regime-switching diffusions and characterizes optimal controls using verification theorems.

Findings

Existence of solutions to the eigenvalue problem under stability conditions

Characterization of optimal stationary Markov controls

Extension to near-monotone cases with principal eigenfunctions

Abstract

In this article, we study the ergodic risk-sensitive control problem for controlled regime-switching diffusions. Under a blanket stability hypothesis, we solve the associated nonlinear eigenvalue problem for weakly coupled systems and characterize the optimal stationary Markov controls via a suitable verification theorem. We also consider the near-monotone case and obtain the existence of principal eigenfunction and optimal stationary Markov controls.