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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. We also 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, the other with "roughly increasing" returns.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2012-31.pdf
File Function: First version, 2012
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Bibliographic Info

Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number DP2012-31.

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Length: 30 pages
Date of creation: Nov 2012
Date of revision:
Handle: RePEc:kob:dpaper:dp2012-31

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Keywords: Dynamic programming; Bellman equation; Value function; Fixed point;

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Cited by:
  1. Yuhki Hosoya & Masayuki Yao, 2013. "A Fixed Point Theorem and an Application to Bellman Operators," Keio/Kyoto Joint Global COE Discussion Paper Series 2012-025, Keio/Kyoto Joint Global COE Program.

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