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Markov decision processes with quasi-hyperbolic discounting

Author

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  • Anna Jaśkiewicz

    (Wrocław University of Science and Technology)

  • Andrzej S. Nowak

    (Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra)

Abstract

We study Markov decision processes with Borel state spaces under quasi-hyperbolic discounting. This type of discounting nicely models human behaviour, which is time-inconsistent in the long run. The decision maker has preferences changing in time. Therefore, the standard approach based on the Bellman optimality principle fails. Within a dynamic game-theoretic framework, we prove the existence of randomised stationary Markov perfect equilibria for a large class of Markov decision processes with transitions having a density function. We also show that randomisation can be restricted to two actions in every state of the process. Moreover, we prove that under some conditions, this equilibrium can be replaced by a deterministic one. For models with countable state spaces, we establish the existence of deterministic Markov perfect equilibria. Many examples are given to illustrate our results, including a portfolio selection model with quasi-hyperbolic discounting.

Suggested Citation

  • Anna Jaśkiewicz & Andrzej S. Nowak, 2021. "Markov decision processes with quasi-hyperbolic discounting," Finance and Stochastics, Springer, vol. 25(2), pages 189-229, April.
    • Handle: RePEc:spr:finsto:v:25:y:2021:i:2:d:10.1007_s00780-020-00443-2
    DOI: 10.1007/s00780-020-00443-2
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    Cited by:

    1. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2022. "Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting," Journal of Economic Theory, Elsevier, vol. 204(C).
    2. Yushi Hamaguchi & Alex S. L. Tse, 2024. "Periodic portfolio selection with quasi-hyperbolic discounting," Papers 2410.18240, arXiv.org.
    3. Jin-Biao Lu & Zhi-Jiang Liu & Dmitry Tulenty & Liudmila Tsvetkova & Sebastian Kot, 2021. "RETRACTED: Implementation of Stochastic Analysis in Corporate Decision-Making Models," Mathematics, MDPI, vol. 9(9), pages 1-16, May.
    4. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.

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    More about this item

    Keywords

    Markov decision process; Markov perfect equilibrium; Stochastic economic growth;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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