Discrete-time control with non-constant discount factor

Héctor Jasso-Fuentes (), José-Luis Menaldi () and Tomás Prieto-Rumeau ()
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Héctor Jasso-Fuentes: CINVESTAV-IPN
José-Luis Menaldi: Wayne State University
Tomás Prieto-Rumeau: UNED

Mathematical Methods of Operations Research, 2020, vol. 92, issue 2, No 6, 377-399

Abstract: Abstract This paper deals with discrete-time Markov decision processes (MDPs) with Borel state and action spaces, and total expected discounted cost optimality criterion. We assume that the discount factor is not constant: it may depend on the state and action; moreover, it can even take the extreme values zero or one. We propose sufficient conditions on the data of the model ensuring the existence of optimal control policies and allowing the characterization of the optimal value function as a solution to the dynamic programming equation. As a particular case of these MDPs with varying discount factor, we study MDPs with stopping, as well as the corresponding optimal stopping times and contact set. We show applications to switching MDPs models and, in particular, we study a pollution accumulation problem.

Keywords: Markov decision processes; Dynamic programming; Optimal stopping problems; 93E20; 34A38; 60J05 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00186-020-00716-8

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