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Discounting long run average growth in stochastic dynamic programs

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Author Info
Jorge Durán

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Abstract

Finding solutions to the Bellman equation often relies on restrictive boundedness assumptions. In this paper we develop a method of proof that allows to dispense with the assumption that returns are bounded from above. In applications our assumptions only imply that long run average (expected) growth is sufficiently discounted, in sharp contrast with classical assumptions either absolutely bounding growth or bounding each period (instead of long run) maximum (instead of average) growth. We discuss our work in relation to the literature and provide several examples. Copyright Springer-Verlag Berlin Heidelberg 2003

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File URL: http://hdl.handle.net/10.1007/s00199-002-0316-5
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Publisher Info
Article provided by Springer in its journal Economic Theory.

Volume (Year): 22 (2003)
Issue (Month): 2 (09)
Pages: 395-413
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Handle: RePEc:spr:joecth:v:22:y:2003:i:2:p:395-413

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Keywords: Keywords and Phrases:Dynamic programming; Weighted norms; Contraction mappings; Dominated convergence; Non additive recursive functions.; JEL Classification Numbers:C61.;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Dutta, Jayasri & Michel, Philippe, 1998. "The Distribution of Wealth with Imperfect Altruism," Journal of Economic Theory, Elsevier, vol. 82(2), pages 379-404, October. [Downloadable!] (restricted)
    Other versions:
  2. Ellen R. McGrattan, 1998. "A defense of AK growth models," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 13-27. [Downloadable!]
  3. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February. [Downloadable!] (restricted)
    Other versions:
  4. Javier Díaz-Giménez & Vincenzo Quadrini & José-Víctor Ríos-Rull, 1997. "Dimensions of inequality: facts on the U.S. distributions of earnings, income, and wealth," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Spr, pages 3-21. [Downloadable!]
  5. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September. [Downloadable!] (restricted)
  6. Jones, Larry E & Manuelli, Rodolfo E, 1990. "A Convex Model of Equilibrium Growth: Theory and Policy Implications," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 1008-38, October. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  8. Ozaki, Hiroyuki & Streufert, Peter A., 1996. "Dynamic programming for non-additive stochastic objectives," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 391-442. [Downloadable!] (restricted)
  9. Streufert, Peter A., 1996. "Biconvergent stochastic dynamic programming, asymptotic impatience, and 'average' growth," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 385-413. [Downloadable!] (restricted)
  10. Loury, Glenn C, 1981. "Intergenerational Transfers and the Distribution of Earnings," Econometrica, Econometric Society, vol. 49(4), pages 843-67, June. [Downloadable!] (restricted)
  11. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Francisco Xavier Lores, 2001. "Cyclical Behaviour Of Consumption Of Non-Durable Goods: Spain Versus U.S.A," Economics Working Papers we014710, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  2. Takashi Kamihigashi, 2006. "Stochastic Optimal Growth with Bounded or Unbounded Utility and with Bounded or Unbounded Shocks," Discussion Paper Series 189, Research Institute for Economics & Business Administration, Kobe University. [Downloadable!]
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