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On Discounted Dynamic Programming with Unbounded Returns

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Author Info
Matkowski, Janusz
Nowak, Andrzej S.
Abstract

In this paper, we apply the idea of $k$-local contraction of \cite{zec, zet} to study discounted stochastic dynamic programming models with unbounded returns. Our main results concern the existence of a unique solution to the Bellman equation and are applied to the theory of stochastic optimal growth. Also a discussion of some subtle issues concerning k-local and global contractions is included.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 12215.

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Date of creation: 13 Oct 2008
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Handle: RePEc:pra:mprapa:12215

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Related research
Keywords: Stochastic dynamic programming; Bellman functional equation; contraction mapping; stochastic optimal growth;

Find related papers by JEL classification:
D90 - Microeconomics - - Intertemporal Choice and Growth - - - General
D91 - Microeconomics - - Intertemporal Choice and Growth - - - Intertemporal Consumer Choice; Life Cycle Models and Saving
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis

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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, Prajit K & Mitra, Tapan, 1989. "On Continuity of the Utility Function in Intertemporal Allocation Models: An Example," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(3), pages 527-36, August. [Downloadable!] (restricted)
  2. Juan Pablo RincÛn-Zapatero & Carlos RodrÌguez-Palmero, 2003. "Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case," Econometrica, Econometric Society, vol. 71(5), pages 1519-1555, 09. [Downloadable!] (restricted)
  3. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June. [Downloadable!] (restricted)
  4. Vailakis, Yiannis & Martins-da-Rocha, V. F., 2008. "Existence and Uniqueness of a Fixed-Point for Local Contractions," Economics Working Papers (Ensaios Economicos da EPGE) 677, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
  5. 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. [Downloadable!] (restricted)
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  6. 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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