An approximation approach to dynamic programming with unbounded returns

Bloise, G., Le Van, C. and Vailakis, Y. (2024) An approximation approach to dynamic programming with unbounded returns. Journal of Mathematical Economics, 111, 102954. (doi: 10.1016/j.jmateco.2024.102954)

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.

• Item Type: Articles
• Additional Information: Gaetano Bloise acknowledges the financial support of the Italian Ministry of Education (PRIN 2022-PXE3B7).
• Keywords: Stochastic recursive utility, Koopmans operator, dynamic programming, Bellman operator multiplicity, uniqueness.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Vailakis, Professor Yiannis

Creator Roles

Vailakis, Y.: Conceptualization, Formal analysis, Investigation, Methodology, Writing – original draft, Writing – review and editing

• Authors: Bloise, G., Le Van, C., and Vailakis, Y.
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Journal of Mathematical Economics
• Publisher: Elsevier
• ISSN: 0304-4068
• ISSN (Online): 1873-1538
• Published Online: 02 February 2024
• Copyright Holders: Copyright © 2024 The Authors
• First Published: First published in Journal of Mathematical Economics 111:102954
• Publisher Policy: Reproduced under a Creative Commons License