IDEAS home Printed from https://ideas.repec.org/p/kob/dpaper/dp2012-05.html
   My bibliography  Save this paper

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

Author

Listed:
  • Takashi Kamihigashi

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

Abstract

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.

Suggested Citation

  • 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.
  • Handle: RePEc:kob:dpaper:dp2012-05
    as

    Download full text from publisher

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Takashi Kamihigashi, 2008. "On the principle of optimality for nonstationary deterministic dynamic programming," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 519-525.
    3. 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, May.
    4. Takashi Kamihigashi, 2011. "Existence and Uniqueness of a Fixed Point for the Bellman Operator in Deterministic Dynamic Programming," Discussion Paper Series DP2011-23, Research Institute for Economics & Business Administration, Kobe University.
    5. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-723, May.
    6. 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, January.
    7. Juan Rincón-Zapatero & Carlos Rodríguez-Palmero, 2007. "Recursive utility with unbounded aggregators," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 381-391, November.
    8. 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, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Philippe Bich & Jean-Pierre Drugeon & Lisa Morhaim, 2015. "On Aggregators and Dynamic Programming," Documents de travail du Centre d'Economie de la Sorbonne 15053, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Takashi Kamihigashi, 2011. "Existence and Uniqueness of a Fixed Point for the Bellman Operator in Deterministic Dynamic Programming," Discussion Paper Series DP2011-23, Research Institute for Economics & Business Administration, Kobe University.
    3. Takashi Kamihigashi & Cuong Le Van, 2015. "Necessary and Sufficient Conditions for a Solution of the Bellman Equation to be the Value Function: A General Principle," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01159177, HAL.
    4. repec:hal:journl:halshs-01169552 is not listed on IDEAS
    5. Philippe Bich & Jean-Pierre Drugeon & Lisa Morhaim, 2015. "On Aggregators and Dynamic Programming," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01169552, HAL.
    6. repec:hal:journl:halshs-01159177 is not listed on IDEAS

    More about this item

    Keywords

    Dynamic programming; Bellman operator; Value function; Fixed point;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kob:dpaper:dp2012-05. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Office of Promoting Research Collaboration, Research Institute for Economics & Business Administration, Kobe University). General contact details of provider: http://edirc.repec.org/data/rikobjp.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.