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On discounted dynamic programming with unbounded returns

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Author Info

  • Janusz Matkowski

    ()

  • Andrzej Nowak

    ()

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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File URL: http://hdl.handle.net/10.1007/s00199-010-0522-5
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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 46 (2011)
Issue (Month): 3 (April)
Pages: 455-474

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Handle: RePEc:spr:joecth:v:46:y:2011:i:3:p:455-474

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Related research

Keywords: Stochastic dynamic programming; Bellman functional equation; Contraction mapping; Stochastic optimal growth; C61; D90; E20;

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References

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  1. Dutta, Prajit K & Sundaram, Rangarajan, 1992. "Markovian Equilibrium in a Class of Stochastic Games: Existence Theorems for Discounted and Undiscounted Models," Economic Theory, Springer, vol. 2(2), pages 197-214, April.
  2. Jorge Durán, 2003. "Discounting long run average growth in stochastic dynamic programs," Economic Theory, Springer, vol. 22(2), pages 395-413, 09.
  3. Rincón-Zapatero, Juan Pablo & Rodríguez-Palmero, C., 2007. "Recursive utility with unbounded aggregators," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/5579, Universidad Carlos III de Madrid.
  4. 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.
  5. V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2010. "Existence and Uniqueness of a Fixed Point for Local Contractions," Econometrica, Econometric Society, vol. 78(3), pages 1127-1141, 05.
  6. 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.
  7. 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.
  8. 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.
  9. Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.
  10. Nowak Andrzej S., 1994. "Zero-Sum Average Payoff Stochastic Games with General State Space," Games and Economic Behavior, Elsevier, vol. 7(2), pages 221-232, September.
  11. Le Van, C. & Morhaim, L., 2000. "Optimal Growth Models with Bounded or Unbounded Returns : a Unifying Approach," Papiers d'Economie Mathématique et Applications 2000.64, Université Panthéon-Sorbonne (Paris 1).
  12. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
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Citations

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Cited by:
  1. Matthias Messner & Nicola Pavoni & Christopher Sleet, 2012. "Contractive Dual Methods for Incentive Problems," Working Papers 466, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  2. V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2010. "Existence and Uniqueness of a Fixed Point for Local Contractions," Econometrica, Econometric Society, vol. 78(3), pages 1127-1141, 05.
  3. Anna Jaśkiewicz & Andrzej Nowak, 2011. "Stochastic Games with Unbounded Payoffs: Applications to Robust Control in Economics," Dynamic Games and Applications, Springer, vol. 1(2), pages 253-279, June.

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