Average optimality for risk-sensitive control with general state space

TL;DR

This paper investigates risk-sensitive average cost control in discrete-time Markov processes with general state spaces, establishing optimality conditions and stationary strategies using a vanishing discount approach.

Contribution

It introduces a new framework for risk-sensitive control with unbounded costs in general state spaces, deriving optimality inequalities and stationary strategies.

Findings

Established optimality inequality for risk-sensitive average cost

Proved existence of optimal stationary strategies

Applied vanishing discount approach to general state spaces

Abstract

This paper deals with discrete-time Markov control processes on a general state space. A long-run risk-sensitive average cost criterion is used as a performance measure. The one-step cost function is nonnegative and possibly unbounded. Using the vanishing discount factor approach, the optimality inequality and an optimal stationary strategy for the decision maker are established.