DO NOT BLAME BELLMAN: IT IS KOOPMANS' FAULT

• 成果类型: Article
• 署名作者: Bloise, Gaetano; Le Van, Cuong; Vailakis, Yiannis
• 署名单位: University of Rome Tor Vergata; Paris School of Economics; IPAG Business School; University of Glasgow
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA20386
• 发表日期: 2024
• 页码: 111-140
• 关键词: Recursive utility; optimal-growth; unbounded returns; FIXED-POINT; uniqueness; EXISTENCE; RISK; substitution; aggregators; consumption

摘要

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.