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On dynamic programming with unbounded returns

Author

Listed:
  • Jorge DurÂn

    (Departament d'Economia i d'HistÔria EconÔmica, Universitat AutÔnoma de Barcelona, E-08193 Bellaterra, SPAIN)

Abstract

Some economic models like those of endogenous growth motivate the analysis of a class of recursive models sharing the property that the return function is not bounded along feasible paths. We consider a strategy of proof which allows to deal with many unbounded recursive models exploiting bounds to the rates of growth rather than to the levels.

Suggested Citation

  • Jorge DurÂn, 2000. "On dynamic programming with unbounded returns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 339-352.
    • Handle: RePEc:spr:joecth:v:15:y:2000:i:2:p:339-352
    Note: Received: December 15, 1997; revised version: April 23, 1999
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    1. Peter A. Streufert, 1990. "Stationary Recursive Utility and Dynamic Programming under the Assumption of Biconvergence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 79-97.
    2. Streufert, Peter A., 1992. "An abstract topological approach to dynamic programming," Journal of Mathematical Economics, Elsevier, vol. 21(1), pages 59-88.
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    Cited by:

    1. Le Van, Cuong & Morhaim, Lisa, 2002. "Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach," Journal of Economic Theory, Elsevier, vol. 105(1), pages 158-187, July.
    2. Ghiglino, Christian, 2002. "Introduction to a General Equilibrium Approach to Economic Growth," Journal of Economic Theory, Elsevier, vol. 105(1), pages 1-17, July.
    3. V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2013. "Fixed point for local contractions: Applications to recursive utility," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 23-33, March.
    4. Bloise, G. & Van, C. Le & Vailakis, Y., 2024. "An approximation approach to dynamic programming with unbounded returns," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    5. Philippe Bich & Jean-Pierre Drugeon & Lisa Morhaim, 2018. "On Temporal Aggregators and Dynamic Programming," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01437496, HAL.
    6. Datta, Manjira & Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2005. "Markovian equilibrium in infinite horizon economies with incomplete markets and public policy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 505-544, August.
    7. Philippe Bich & Jean-Pierre Drugeon & Lisa Morhaim, 2018. "On temporal aggregators and dynamic programming," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 787-817, October.
    8. Jorge Durán, 2003. "Discounting long run average growth in stochastic dynamic programs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(2), pages 395-413, September.
    9. Le Van, Cuong & Cagri Saglam, H., 2004. "Optimal growth models and the Lagrange multiplier," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 393-410, June.
    10. Takashi Kamihigashi, 2014. "Elementary results on solutions to the bellman equation of dynamic programming: existence, uniqueness, and convergence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 251-273, June.
    11. Jean-Pierre Drugeon & Thai Ha-Huy & Thi Do Hanh Nguyen, 2019. "On maximin dynamic programming and the rate of discount," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 703-729, April.
    12. Le Van, Cuong & Vailakis, Yiannis, 2005. "Recursive utility and optimal growth with bounded or unbounded returns," Journal of Economic Theory, Elsevier, vol. 123(2), pages 187-209, August.
    13. Suen, Richard M. H., 2009. "Bounding the CRRA Utility Functions," MPRA Paper 13260, University Library of Munich, Germany.
    14. Takashi Kamihigashi, 2014. "An order-theoretic approach to dynamic programming: an exposition," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 13-21, April.
    15. Matthias Messner & Nicola Pavoni & Christopher Sleet, "undated". "Contractive Dual Methods for Incentive Problems," GSIA Working Papers 2012-E26, Carnegie Mellon University, Tepper School of Business.
    16. Bäuerle, Nicole & Jaśkiewicz, Anna, 2018. "Stochastic optimal growth model with risk sensitive preferences," Journal of Economic Theory, Elsevier, vol. 173(C), pages 181-200.
    17. Cuong Le Van & Lisa Morhaim & Yiannis Vailakis, 2008. "Monotone Concave Operators: An application to the existence and uniqueness of solutions to the Bellman equation," Working Papers hal-00294828, HAL.
    18. Cuong Le Van & Lisa Morhaim & Yiannis Vailakis, 2008. "Monotone concave operators: An application to the existence and uniqueness of solutions to the Bellman equation," Discussion Papers 0803, University of Exeter, Department of Economics.
    19. Łukasz Balbus & Anna Jaśkiewicz & Andrzej S. Nowak, 2020. "Equilibria in Altruistic Economic Growth Models," Dynamic Games and Applications, Springer, vol. 10(1), pages 1-18, March.
    20. Bloise, Gaetano & Vailakis, Yiannis, 2018. "Convex dynamic programming with (bounded) recursive utility," Journal of Economic Theory, Elsevier, vol. 173(C), pages 118-141.
    21. 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.
    22. Le Van, Cuong & Cagri Saglam, H., 2004. "Optimal growth models and the Lagrange multiplier," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 393-410, June.
    23. Gaetano Bloise & Cuong Le Van & Yiannis Vailakis, 2024. "Do not Blame Bellman: It Is Koopmans' Fault," Econometrica, Econometric Society, vol. 92(1), pages 111-140, January.

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    More about this item

    Keywords

    Dynamic programming; Unbounded returns; Non additive objective.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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