Do not Blame Bellman: It Is Koopmans' Fault

IF 6.6 1区经济学 Q1 ECONOMICS

Econometrica Pub Date : 2024-01-30 DOI:10.3982/ECTA20386

Gaetano Bloise, Cuong Le Van, Yiannis Vailakis

引用次数: 0

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.

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不要责怪贝尔曼：这是库普曼斯的错

我们基于塔尔斯基定点定理的基本应用，为递归效用随机动态程序设计提供了一种统一的方法。我们确定，多重值的唯一来源是存在多个与给定聚合器一致的递归效用，每个效用都能产生递归程序的合法值。我们还提出了在某些情况下确保递归程序唯一值的充分条件。总之，在承认唯一性在一般情况下不可避免地失效的同时，我们认为贝尔曼算子的最大定点应享有特权地位。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Econometrica 社会科学-数学跨学科应用

CiteScore

11.00

自引率

3.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Econometrica publishes original articles in all branches of economics - theoretical and empirical, abstract and applied, providing wide-ranging coverage across the subject area. It promotes studies that aim at the unification of the theoretical-quantitative and the empirical-quantitative approach to economic problems and that are penetrated by constructive and rigorous thinking. It explores a unique range of topics each year - from the frontier of theoretical developments in many new and important areas, to research on current and applied economic problems, to methodologically innovative, theoretical and applied studies in econometrics. Econometrica maintains a long tradition that submitted articles are refereed carefully and that detailed and thoughtful referee reports are provided to the author as an aid to scientific research, thus ensuring the high calibre of papers found in Econometrica. An international board of editors, together with the referees it has selected, has succeeded in substantially reducing editorial turnaround time, thereby encouraging submissions of the highest quality. We strongly encourage recent Ph. D. graduates to submit their work to Econometrica. Our policy is to take into account the fact that recent graduates are less experienced in the process of writing and submitting papers.