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Persistently optimal policies in stochastic dynamic programming with generalized discounting

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

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.

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File URL: http://mpra.ub.uni-muenchen.de/31755/1/MPRA_paper_31755.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 31755.

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Date of creation: 21 Jun 2011
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Handle: RePEc:pra:mprapa:31755
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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. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
  3. 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.
  4. Grandmont, Jean-Michel, 1977. "Temporary General Equilibrium Theory," Econometrica, Econometric Society, vol. 45(3), pages 535-72, April.
  5. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
  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. 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.
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