Elementary results on solutions to the bellman equation of dynamic programming: existence, uniqueness, and convergence

Takashi Kamihigashi

Economic Theory, 2014, vol. 56, issue 2, 273 pages

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Dynamic programming; Bellman equation; Value function; Fixed point; C61 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (27)

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Working Paper: Elementary Results on Solutions to the Bellman Equation of Dynamic Programming:Existence, Uniqueness, and Convergence (2013)
Working Paper: Elementary Results on Solutions to the Bellman Equation of Dynamic Programming: Existence, Uniqueness, and Convergence (2012)
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DOI: 10.1007/s00199-013-0789-4

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