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On Dynamic Programming with Unbounded Rewards

Author

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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
    DOI: 10.1287/mnsc.21.11.1225
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    Cited by:

    1. Ilbin Lee & Marina A. Epelman & H. Edwin Romeijn & Robert L. Smith, 2017. "Simplex Algorithm for Countable-State Discounted Markov Decision Processes," Operations Research, INFORMS, vol. 65(4), pages 1029-1042, August.
    2. Hyun-Soo Ahn & Mehmet Gümüc{s} & Philip Kaminsky, 2009. "Inventory, Discounts, and the Timing Effect," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 613-629, September.
    3. 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.
    4. C. Drent & S. Kapodistria & J. A. C. Resing, 2019. "Condition-based maintenance policies under imperfect maintenance at scheduled and unscheduled opportunities," Queueing Systems: Theory and Applications, Springer, vol. 93(3), pages 269-308, December.
    5. James E. Smith & Kevin F. McCardle, 1998. "Valuing Oil Properties: Integrating Option Pricing and Decision Analysis Approaches," Operations Research, INFORMS, vol. 46(2), pages 198-217, April.
    6. José Niño-Mora, 2020. "A Verification Theorem for Threshold-Indexability of Real-State Discounted Restless Bandits," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 465-496, May.
    7. Otero, Karina V., 2016. "Nonparametric identification of dynamic multinomial choice games: unknown payoffs and shocks without interchangeability," MPRA Paper 86784, University Library of Munich, Germany.
    8. Alexis Akira Toda, 2024. "Unbounded Markov dynamic programming with weighted supremum norm Perov contractions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 141-156, December.
    9. Sturm, Roland, 1995. "Why does nuclear power performance differ across Europe?," European Economic Review, Elsevier, vol. 39(6), pages 1197-1214, June.
    10. James E. Smith & Canan Ulu, 2012. "Technology Adoption with Uncertain Future Costs and Quality," Operations Research, INFORMS, vol. 60(2), pages 262-274, April.
    11. Hong Chen & Murray Zed Frank, 2022. "Equilibrium Defaultable Corporate Debt and Investment," Papers 2202.05885, arXiv.org.

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