On the policy improvement algorithm for ergodic risk-sensitive control

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.

Automated summary

This article discusses the ergodic risk-sensitive control problem for a class of multidimensional controlled diffusions on the entire space. The study includes minimization and maximization problems under different stability assumptions and a near-monotone assumption on the running cost. It establishes the convergence of the policy improvement algorithm for these models and presents a more general result on the equilibrium's region of attraction.