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Do not Blame Bellman: It Is Koopmans' Fault

Author

Listed:
  • Gaetano Bloise

    (University of Rome II)

  • Cuong Le Van

    (IPAG Business School, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Yiannis Vailakis

    (University of Glasgow)

Abstract

We provide a unified approach to stochastic dynamic programming with recursive utility based on an elementary application of Tarski's fixed point theorem. We establish that the exclusive source of multiple values is the presence of multiple recursive utilities consistent with the given aggregator, each yielding a legitimate value of the recursive program. We also present sufficient conditions ensuring a unique value of the recursive program in some circumstances. Overall, acknowledging the unavoidable failure of uniqueness in general, we argue that the greatest fixed point of the Bellman operator should have a privileged position.

Suggested Citation

  • Gaetano Bloise & Cuong Le Van & Yiannis Vailakis, 2024. "Do not Blame Bellman: It Is Koopmans' Fault," Post-Print halshs-04928565, HAL.
  • Handle: RePEc:hal:journl:halshs-04928565
    DOI: 10.3982/ECTA20386
    as

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