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

Takashi Kamihigashi

No DP2013-35, Discussion Paper Series from Research Institute for Economics & Business Administration, Kobe University

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.

Keywords: Dynamic programming; Bellman equation; value function; xed point (search for similar items in EconPapers)
JEL-codes: C61 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2013-11, Revised 2013-12
New Economics Papers: this item is included in nep-dge
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Citations: View citations in EconPapers (2)

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https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2013-35.pdf Revised version, 2013 (application/pdf)

Related works:
Journal Article: Elementary results on solutions to the bellman equation of dynamic programming: existence, uniqueness, and convergence (2014)
Working Paper: Elementary Results on Solutions to the Bellman Equation of Dynamic Programming: Existence, Uniqueness, and Convergence (2012)
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