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Markov control processes with randomized discounted cost. (English) Zbl 1126.90075

Summary: In this paper we consider Markov decision processes with discounted cost and a random rate in Borel spaces. We establish the dynamic programming algorithm in finite and infinite horizon cases. We provide conditions for the existence of measurable selectors. And we show an example of consumption-investment problem.

MSC:

90C40 Markov and semi-Markov decision processes
93E20 Optimal stochastic control
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