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Monotone Concave Operators: An application to the existence and uniqueness of solutions to the Bellman equation

Author

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  • Cuong Le Van

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Lisa Morhaim

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, IMB - Institut de Mathématiques de Bourgogne [Dijon] - UB - Université de Bourgogne - CNRS - Centre National de la Recherche Scientifique)

  • Yiannis Vailakis

    (School of Business and Economics - University of Exeter)

Abstract

We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel'skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.

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  • Cuong Le Van & Lisa Morhaim & Yiannis Vailakis, 2008. "Monotone Concave Operators: An application to the existence and uniqueness of solutions to the Bellman equation," Working Papers hal-00294828, HAL.
    • Handle: RePEc:hal:wpaper:hal-00294828
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    References listed on IDEAS

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    Cited by:

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    3. Paweł Dziewulski, 2011. "On Time-to-Build Economies with Multiple-Stage Investments," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 9, pages 23-49.
    4. Jing Guo & Xue Dong He, 2021. "Recursive Utility with Investment Gains and Losses: Existence, Uniqueness, and Convergence," Papers 2107.05163, arXiv.org.
    5. Massimo Marinacci & Luigi Montrucchio, 2017. "Unique Tarski Fixed Points," Working Papers 604, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    6. Robert Becker & Juan Pablo Rincon-Zapatero, 2018. "Recursive Utility and Thompson Aggregators, II: Uniqueness of the Recursive Utility Representation," CAEPR Working Papers 2018-008, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    7. Gaetano Bloise, 2013. "The structure of competitive equilibrium with unsecured debt," Departmental Working Papers of Economics - University 'Roma Tre' 0187, Department of Economics - University Roma Tre.

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