On Maximin Optimization Problems & the Rate of Discount: a Simple Dynamic Programming Argument

Jean-Pierre Drugeon (), Thai Ha-Huy and Thi-Do-Hanh Nguyen ()
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Jean-Pierre Drugeon: PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique
Thi-Do-Hanh Nguyen: VMU - Vietnam Maritime University [Hai Phon]

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Abstract: This article establishes a dynamic programming argument for a maximin optimization problem where the agent completes a minimization over a set of discount rates. Even though the consideration of a maximin criterion results in a program that is not convex and not stationary over time, it is proved that a careful reference to extended dynamic programming principles and a maxmin functional equation however allows for circumventing these difficulties and recovering an optimal sequence that is time consistent. This in its turn brings about a stationary dynamic programming argument.

Keywords: Maximin principle; Non-convexities; Value fun-ion; Policy fun-ion; Supermodularity (search for similar items in EconPapers)
Date: 2018-04
New Economics Papers: this item is included in nep-mic and nep-sea
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01761997v2
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