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

Tomás Prieto-Rumeau () and Onésimo Hernández-Lerma

Mathematical Methods of Operations Research, 2009, vol. 70, issue 3, 527-540

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

Keywords: Continuous-time controlled Markov chains; Markov decision processes; Average reward optimality; Overtaking optimality; Average variance; 93E20; 90C40; 60J27 (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s00186-008-0276-z

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