Blackwell Optimality in the Class of Markov Policies for Continuous-Time Controlled Markov Chains

Abstract

This paper deals with Blackwell optimality for continuous-time controlled Markov chains with compact Borel action space, and possibly unbounded reward (or cost) rates and unbounded transition rates. We prove the existence of a deterministic stationary policy which is Blackwell optimal in the class of all admissible (nonstationary) Markov policies, thus extending previous results that analyzed Blackwell optimality in the class of stationary policies. We compare our assumptions to the corresponding ones for discrete-time Markov controlled processes.