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Variance minimization and the overtaking optimality approach to continuous-time controlled Markov chains. (English) Zbl 1177.93101

Summary: 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).

MSC:

93E20 Optimal stochastic control
90C40 Markov and semi-Markov decision processes
60J25 Continuous-time Markov processes on general state spaces
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