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Discounting Long Run Average Growth In Stochastic Dynamic Programs

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  • Jorge Durán

    ()
    (Universidad de Alicante)

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.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2002-08.pdf
File Function: Fisrt version / Primera version, 2002
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2002-08.

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Length: 40 pages
Date of creation: Jul 2002
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2002-08

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Related research

Keywords: Dynamic Programming; Weighted Norms; Contraction Mappings; Dominated Convergence; Non Additive Recursive Functions.;

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References

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  1. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
  2. 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.
  3. DUTTA, Jayasri & MICHEL, Philippe, 1995. "The Distribution of Wealth with Imperfect Altruism," CORE Discussion Papers 1995058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Robert E. Lucas Jr. & Nancy L. Stokey, 1982. "Optimal Growth with Many Consumers," Discussion Papers 518, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. 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.
  6. Ozaki, Hiroyuki & Streufert, Peter A., 1996. "Dynamic programming for non-additive stochastic objectives," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 391-442.
  7. Ellen R. McGrattan, 1998. "A defense of AK growth models," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 13-27.
  8. 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.
  9. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
  10. 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.
  11. Loury, Glenn C, 1981. "Intergenerational Transfers and the Distribution of Earnings," Econometrica, Econometric Society, vol. 49(4), pages 843-67, June.
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Cited by:
  1. 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.
  2. LE VAN, Cuong & VAILAKIS, Yiannis, 2002. "Recursive utility and optimal growth with bounded or unbounded returns," CORE Discussion Papers 2002055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Janusz Matkowski & Andrzej Nowak, 2011. "On discounted dynamic programming with unbounded returns," Economic Theory, Springer, vol. 46(3), pages 455-474, April.
  4. 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.

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