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On Dynamic Programming with Unbounded Rewards

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  • Steven A. Lippman

    (University of California, Los Angeles)

Abstract

Using the technique employed by the author in an earlier paper, the existence of an optimal stationary policy that can be obtained from the usual functional equation is again established in the presence of a bound (not necessarily polynomial) on the one-period reward of a semi-Markov decision process. This is done for both the discounted and the average cost case. In addition to allowing an uncountable state space, the law of motion of the system is rather general in that we permit any state to be reached in a single transition. There is, however, a bound on a weighted moment of the next state reached. Finally, we indicate the applicability of these results.

Suggested Citation

  • Steven A. Lippman, 1975. "On Dynamic Programming with Unbounded Rewards," Management Science, INFORMS, vol. 21(11), pages 1225-1233, July.
  • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:11:p:1225-1233
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    File URL: http://dx.doi.org/10.1287/mnsc.21.11.1225
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    References listed on IDEAS

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    1. Jacob A. Mincer & Victor Zarnowitz, 1969. "The Evaluation of Economic Forecasts," NBER Chapters,in: Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance, pages 3-46 National Bureau of Economic Research, Inc.
    2. N/A, 1962. "Summary," National Institute Economic Review, National Institute of Economic and Social Research, vol. 19(1), pages 3-3, February.
    3. N/A, 1962. "Summary," National Institute Economic Review, National Institute of Economic and Social Research, vol. 20(1), pages 3-3, May.
    4. N/A, 1962. "Summary," National Institute Economic Review, National Institute of Economic and Social Research, vol. 21(1), pages 3-3, August.
    5. J. G. Cragg & Burton G. Malkiel, 1968. "The Consensus And Accuracy Of Some Predictions Of The Growth Of Corporate Earnings," Journal of Finance, American Finance Association, vol. 23(1), pages 67-84, March.
    6. N/A, 1962. "Summary," National Institute Economic Review, National Institute of Economic and Social Research, vol. 22(1), pages 3-3, November.
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    Cited by:

    1. Hyun-Soo Ahn & Mehmet Gümüc{s} & Philip Kaminsky, 2009. "Inventory, Discounts, and the Timing Effect," Manufacturing & Service Operations Management, INFORMS, pages 613-629.
    2. Andriy Norets, 2010. "Continuity and differentiability of expected value functions in dynamic discrete choice models," Quantitative Economics, Econometric Society, vol. 1(2), pages 305-322, November.
    3. Sturm, Roland, 1995. "Why does nuclear power performance differ across Europe?," European Economic Review, Elsevier, vol. 39(6), pages 1197-1214, June.

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