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Existence and uniqueness of solutions to the Bellman equation in stochastic dynamic programming

Author

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  • Rincón-Zapatero, Juan Pablo

    (Departamento de Economía. Universidad Carlos III de Madrid)

Abstract

In this paper we develop a framework to analyze stochastic dynamic optimization problems in discrete time. We obtain new results about the existence and uniqueness of solutions to the Bellman equation through a notion of Banach contractions that generalizes known results for Banach and local contractions. We apply the results obtained to an endogenous growth model and compare our approach with other well known methods, such as the weighted contraction method, countable local contractions and the Q-transform.

Suggested Citation

  • Rincón-Zapatero, Juan Pablo, 2024. "Existence and uniqueness of solutions to the Bellman equation in stochastic dynamic programming," Theoretical Economics, Econometric Society, vol. 19(3), July.
    • Handle: RePEc:the:publsh:5161
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    References listed on IDEAS

    as
    1. Kamihigashi, Takashi, 2007. "Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 477-500, April.
    2. Kaushik Mitra, 1998. "On capital accumulation paths in a neoclassical stochastic growth model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 457-464.
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    More about this item

    Keywords

    Stochastic dynamic programming; Bellman equation; contraction mapping; weighted contraction; local contraction; Q-transform; endogenous growth;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)

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