Continuous-time Markov decision processes under the risk-sensitive average cost criterion

TL;DR

This paper investigates continuous-time Markov decision processes with a focus on risk-sensitive average costs, establishing conditions for optimal policies and solving the associated optimality equation.

Contribution

It introduces a new approach to prove the existence of solutions and optimal policies for risk-sensitive average cost criteria in continuous-time MDPs with finite states.

Findings

Existence of solutions to the risk-sensitive average cost optimality equation.

Existence of optimal deterministic stationary policies.

Applicable under mild conditions for bounded costs and transition rates.

Abstract

This paper studies continuous-time Markov decision processes under the risk-sensitive average cost criterion. The state space is a finite set, the action space is a Borel space, the cost and transition rates are bounded, and the risk-sensitivity coefficient can take arbitrary positive real numbers. Under the mild conditions, we develop a new approach to establish the existence of a solution to the risk-sensitive average cost optimality equation and obtain the existence of an optimal deterministic stationary policy.