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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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References

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  1. 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.
  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. Matkowski, Janusz & Nowak, Andrzej S., 2008. "On Discounted Dynamic Programming with Unbounded Returns," MPRA Paper 12215, University Library of Munich, Germany.
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Cited by:
  1. Matkowski, Janusz & Nowak, Andrzej S., 2008. "On Discounted Dynamic Programming with Unbounded Returns," MPRA Paper 12215, University Library of Munich, Germany.
  2. 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.
  3. Takashi Kamihigashi, 2012. "Elementary Results on Solutions to the Bellman Equation of Dynamic Programming: Existence, Uniqueness, and Convergence," Discussion Paper Series DP2012-31, Research Institute for Economics & Business Administration, Kobe University.
  4. 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.
  5. 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.
  6. 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.

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