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Recursive Utility and the Solution to the Bellman Equation

Author

Listed:
  • Masayuki Yao

    (Research Associate (Non-tenured), Department of Economics, Keio University)

Abstract

This study infinite-horizon deterministic dynamic programming problems based on recursive utility in discrete time. Under a small number of conditions, we show that the Bellman operator has a fixed point using Knaster-Tarski's fixed point theorem. We also show the fixed point of the Bellman operator can be computed by iteration from the initial function between the lower boundary and the fixed point. To show the convergence theorem, we use Tarski-Kantorovitch's fixed point theorem.

Suggested Citation

  • Masayuki Yao, 2016. "Recursive Utility and the Solution to the Bellman Equation," Discussion Paper Series DP2016-08, Research Institute for Economics & Business Administration, Kobe University.
    • Handle: RePEc:kob:dpaper:dp2016-08
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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2016-08.pdf
    File Function: First version, 2016
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Philippe Bich & Jean-Pierre Drugeon & Lisa Morhaim, 2018. "On Temporal Aggregators and Dynamic Programming," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01437496, HAL.
    2. Philippe Bich & Jean-Pierre Drugeon & Lisa Morhaim, 2018. "On temporal aggregators and dynamic programming," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 787-817, October.

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    More about this item

    Keywords

    Recursive utility; Fixed point theorem; Dynamic programming; Bellman equation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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