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Elementary Results on Solutions to the Bellman Equation of Dynamic Programming:Existence, Uniqueness, and Convergence

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  • Takashi Kamihigashi

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

Abstract

We establish some elementary results on solutions to the Bellman equation without introducing any topological assumption. Under a small number of conditions, we show that the Bellman equation has a unique solution in a certain set, that this solution is the value function, and that the value function can be computed by value iteration with an appropriate initial condition. In addition, we show that the value function can be computed by the same procedure under alternative conditions. We apply our results to two optimal growth models: one with a discontinuous production function and the other with \roughly increasing" returns.

Suggested Citation

  • Takashi Kamihigashi, 2013. "Elementary Results on Solutions to the Bellman Equation of Dynamic Programming:Existence, Uniqueness, and Convergence," Discussion Paper Series DP2013-35, Research Institute for Economics & Business Administration, Kobe University, revised Dec 2013.
    • Handle: RePEc:kob:dpaper:dp2013-35
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    More about this item

    Keywords

    Dynamic programming; Bellman equation; value function; xed point;
    All these keywords.

    JEL classification:

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

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