The Laurent series, sensitive discount and Blackwell optimality for continuous-time controlled Markov chains

Abstract

This paper gives conditions for the convergence of the Laurent series expansion for a class of continuous-time controlled Markov chains with possibly unbounded reward (or cost) rates and unbounded transition rates. That series is then used to study several optimization criteria, including n-discount optimality (for n=−1,0,1,...), Blackwell optimality, and the maximization of a certain vector criterion that in particular gives gain and bias optimality.