Ergodic risk-sensitive control for regime-switching diffusions

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.