Do not blame Bellman: it is Koopmans' fault

Bloise, G., Le Van, C. and Vailakis, Y. (2024) Do not blame Bellman: it is Koopmans' fault. Econometrica, 92(1), pp. 111-140. (doi: 10.3982/ECTA20386)

Abstract

We provide a unified approach to stochastic dynamic programming with recursive utility based on an elementary application of Tarski's fixed point theorem. We establish that the exclusive source of multiple values is the presence of multiple recursive utilities consistent with the given aggregator, each yielding a legitimate value of the recursive program. We also present sufficient conditions ensuring a unique value of the recursive program in some circumstances. Overall, acknowledging the unavoidable failure of uniqueness in general, we argue that the greatest fixed point of the Bellman operator should have a privileged position.

• Item Type: Articles
• Additional Information: Research Funding: Italian Ministry of Education. Grant Number: 2015 Ideas. Grant Number: 240983
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Vailakis, Professor Yiannis
• Authors: Bloise, G., Le Van, C., and Vailakis, Y.
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Econometrica
• Publisher: Wiley
• ISSN: 0012-9682
• ISSN (Online): 1468-0262
• Published Online: 30 January 2024
• Copyright Holders: Copyright © 2024 The Authors
• First Published: First published in Econometrica 92(1): 111-140
• Publisher Policy: Reproduced under a Creative Commons License