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Discrete-time control with non-constant discount factor

Author

Listed:
  • Héctor Jasso-Fuentes

    (CINVESTAV-IPN)

  • José-Luis Menaldi

    (Wayne State University)

  • Tomás Prieto-Rumeau

    (UNED)

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.

Suggested Citation

  • Héctor Jasso-Fuentes & José-Luis Menaldi & Tomás Prieto-Rumeau, 2020. "Discrete-time control with non-constant discount factor," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(2), pages 377-399, October.
    • Handle: RePEc:spr:mathme:v:92:y:2020:i:2:d:10.1007_s00186-020-00716-8
    DOI: 10.1007/s00186-020-00716-8
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    References listed on IDEAS

    as
    1. Rieder, Ulrich, 1975. "On stopped decision processes with discrete time parameter," Stochastic Processes and their Applications, Elsevier, vol. 3(4), pages 365-383, October.
    2. Morimoto,Hiroaki, 2010. "Stochastic Control and Mathematical Modeling," Cambridge Books, Cambridge University Press, number 9780521195034.
    3. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, November.
    Full references (including those not matched with items on IDEAS)

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