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Existence and Uniqueness of a Fixed Point for the Bellman Operator in Deterministic Dynamic Programming

  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

We study existence and uniqueness of a fixed point for the Bellman operator in deterministic dynamic programming. Without any topological assumption, we show that the Bellman operator has a unique fixed point in a restricted domain, that this fixed point is the value function, and that the value function can be computed by value iteration.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2012-05.pdf
File Function: First version, 2012
Download Restriction: no

Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number DP2012-05.

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Length: 14 pages
Date of creation: Feb 2012
Date of revision:
Handle: RePEc:kob:dpaper:dp2012-05
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Web page: http://www.rieb.kobe-u.ac.jp/index-e.html

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  1. LE VAN, Cuong & MORHAIM, Lisa, 2001. "Optimal growth models with bounded or unbounded returns: a unifying approach," CORE Discussion Papers 2001034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Takashi Kamihigashi, 2007. "On the Principle of Optimality for Nonstationary Deterministic Dynamic Programming," Discussion Paper Series 200, Research Institute for Economics & Business Administration, Kobe University.
  3. 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.
  4. 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.
  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. Juan Rincón-Zapatero & Carlos Rodríguez-Palmero, 2007. "Recursive utility with unbounded aggregators," Economic Theory, Springer, vol. 33(2), pages 381-391, November.
  7. Juan Pablo Rincón-Zapatero & Carlos Rodríguez-Palmero, 2009. "Corrigendum to "Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case" Econometrica, Vol. 71, No. 5 (September, 2003), 1519-1555," Econometrica, Econometric Society, vol. 77(1), pages 317-318, 01.
  8. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-23, May.
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