An approximation approach to dynamic programming with unbounded returns

G. Bloise, C. Le Van and Y. Vailakis

Journal of Mathematical Economics, 2024, vol. 111, issue C

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.

Keywords: Stochastic recursive utility; Koopmans operator; Dynamic programming; Bellman operator; Multiplicity; Uniqueness (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:111:y:2024:i:c:s0304406824000168

DOI: 10.1016/j.jmateco.2024.102954

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