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

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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).

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Authors and Affiliations

  1. Departamento de Estadística, Facultad de Ciencias, UNED, Calle Senda del Rey 9, 28040, Madrid, Spain

    Tomás Prieto-Rumeau

  2. Departamento de Matemáticas, CINVESTAV-IPN, Mexico D.F., Mexico

    Onésimo Hernández-Lerma

Authors
  1. Tomás Prieto-Rumeau
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  2. Onésimo Hernández-Lerma
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Corresponding author

Correspondence to Tomás Prieto-Rumeau.

Additional information

This research was partially supported by CONACyT Grant 45693-F.

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Prieto-Rumeau, T., Hernández-Lerma, O. Variance minimization and the overtaking optimality approach to continuous-time controlled Markov chains. Math Meth Oper Res 70, 527–540 (2009). https://doi.org/10.1007/s00186-008-0276-z

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  • DOI: https://doi.org/10.1007/s00186-008-0276-z

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