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Existence and Uniqueness of a Fixed Point for Local Contractions

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  • V. Filipe Martins-da-Rocha
  • Yiannis Vailakis

Abstract

This paper proves the existence and uniqueness of a fixed point for local contractions without assuming the family of contraction coefficients to be uniformly bounded away from 1. More importantly it shows how this fixed-point result can apply to study the existence and uniqueness of solutions to some recursive equations that arise in economic dynamics. Copyright 2010 The Econometric Society.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 78 (2010)
Issue (Month): 3 (05)
Pages: 1127-1141

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Handle: RePEc:ecm:emetrp:v:78:y:2010:i:3:p:1127-1141

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  1. Janusz Matkowski & Andrzej Nowak, 2011. "On discounted dynamic programming with unbounded returns," Economic Theory, Springer, vol. 46(3), pages 455-474, April.
  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.
  3. Juan Rincón-Zapatero & Carlos Rodríguez-Palmero, 2007. "Recursive utility with unbounded aggregators," Economic Theory, Springer, vol. 33(2), pages 381-391, November.
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Cited by:
  1. Janusz Matkowski & Andrzej Nowak, 2011. "On discounted dynamic programming with unbounded returns," Economic Theory, Springer, vol. 46(3), pages 455-474, April.
  2. Takashi Kamihigashi, 2013. "Elementary Results on Solutions to the Bellman Equation of Dynamic Programming:Existence, Uniqueness, and Convergence," Discussion Paper Series DP2013-35, Research Institute for Economics & Business Administration, Kobe University, revised Dec 2013.
  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.
  4. 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.
  5. Takashi Kamihigashi, 2012. "Existence and Uniqueness of a Fixed Point for the Bellman Operator in Deterministic Dynamic Programming," Discussion Paper Series DP2012-05, Research Institute for Economics & Business Administration, Kobe University.
  6. Takashi Kamihigashi, 2014. "Elementary results on solutions to the bellman equation of dynamic programming: existence, uniqueness, and convergence," Economic Theory, Springer, vol. 56(2), pages 251-273, June.
  7. Takashi Kamihigashi, 2013. "An Order-Theoretic Approach to Dynamic Programming: An Exposition," Discussion Paper Series DP2013-29, Research Institute for Economics & Business Administration, Kobe University, revised Nov 2013.
  8. Jenö Pál & John Stachurski, 2011. "Fitted Value Function Iteration With Probability One Contractions," ANU Working Papers in Economics and Econometrics 2011-560, Australian National University, College of Business and Economics, School of Economics.

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