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Variance minimization and the overtaking optimality approach to continuous-time controlled Markov chains

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  • Tomás Prieto-Rumeau
  • Onésimo Hernández-Lerma

Abstract

This paper deals with denumerable-state continuous-time controlled Markov chains with possibly unbounded transition and reward rates. It concerns optimality criteria that improve the usual expected average reward criterion. First, we show the existence of average reward optimal policies with minimal average variance. Then we compare the variance minimization criterion with overtaking optimality. We present an example showing that they are opposite criteria, and therefore we cannot optimize them simultaneously. This leads to a multiobjective problem for which we identify the set of Pareto optimal policies (also known as nondominated policies). Copyright Springer-Verlag 2009

Suggested Citation

  • Tomás Prieto-Rumeau & Onésimo Hernández-Lerma, 2009. "Variance minimization and the overtaking optimality approach to continuous-time controlled Markov chains," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 527-540, December.
    • Handle: RePEc:spr:mathme:v:70:y:2009:i:3:p:527-540
    DOI: 10.1007/s00186-008-0276-z
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    1. Tomás Prieto-Rumeau & Onésimo Hernández-Lerma, 2005. "The Laurent series, sensitive discount and Blackwell optimality for continuous-time controlled Markov chains," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(1), pages 123-145, March.
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    1. Tomás Prieto-Rumeau & Onésimo Hernández-Lerma, 2016. "Uniform ergodicity of continuous-time controlled Markov chains: A survey and new results," Annals of Operations Research, Springer, vol. 241(1), pages 249-293, June.

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