An approximation approach to dynamic programming with unbounded returns

Gaetano Bloise, Cuong Le Van () and Yiannis Vailakis ()
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Gaetano Bloise: University of Rome II
Cuong Le Van: 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 nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, IPAG Business School
Yiannis Vailakis: University of Glasgow

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Abstract: We study stochastic dynamic programming with recursive utility in settings where multiplicity of values is only attributed to unbounded returns. That is, we consider Koopmans aggregators that, when artificially restricted to be bounded, satisfy the traditional Blackwell's discounting condition (as it certainly happens with time-additive aggregators). We argue that, when the truncation is removed, the sequence of truncated values converges to the relevant fixed point of the untruncated Bellman operator, whenever it exists, and diverges otherwise. The experiment provides a natural selection criterion, corresponding to an extension of the recursive utility from bounded to unbounded returns.

Date: 2024-04
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Published in Journal of Mathematical Economics, 2024, 111, ⟨10.1016/j.jmateco.2024.102954⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04934128

DOI: 10.1016/j.jmateco.2024.102954

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