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Persistently optimal policies in stochastic dynamic programming with generalized discounting

Author

Listed:
  • Jaśkiewicz, Anna
  • Matkowski, Janusz
  • Nowak, Andrzej S.

Abstract

In this paper we study a Markov decision process with a non-linear discount function. Our approach is in spirit of the von Neumann-Morgenstern concept and is based on the notion of expectation. First, we define a utility on the space of trajectories of the process in the finite and infinite time horizon and then take their expected values. It turns out that the associated optimization problem leads to a non-stationary dynamic programming and an infinite system of Bellman equations, which result in obtaining persistently optimal policies. Our theory is enriched by examples.

Suggested Citation

  • Jaśkiewicz, Anna & Matkowski, Janusz & Nowak, Andrzej S., 2011. "Persistently optimal policies in stochastic dynamic programming with generalized discounting," MPRA Paper 31755, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:31755
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    References listed on IDEAS

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    1. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February.
    2. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
    3. Grandmont, Jean-Michel, 1993. "Temporary general equilibrium theory," Handbook of Mathematical Economics,in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922 Elsevier.
    4. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
    5. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
    6. Schäl, Manfred, 1975. "On dynamic programming: Compactness of the space of policies," Stochastic Processes and their Applications, Elsevier, vol. 3(4), pages 345-364, October.
    7. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
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    More about this item

    Keywords

    Stochastic dynamic programming; Persistently optimal policies; Variable discounting; Bellman equation; Resource extraction; Growth theory;

    JEL classification:

    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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