Existence and uniqueness of solutions to the Bellman equation in stochastic dynamic programming

• 成果类型: Article
• 署名作者: Pablo Rincon-Zapatero, Juan
• 署名单位: Universidad Carlos III de Madrid
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE5161
• 发表日期: 2024-07-01
• 页码: 1223-1260
• 关键词: Stochastic dynamic programming; Bellman equation; contraction mapping; weighted contraction; local contraction; Q-transform; endogenous growth; C61; E21

摘要

In this paper, we develop a framework to analyze stochastic dynamic optimization problems in discrete time. We obtain new results about the existence and uniqueness of solutions to the Bellman equation through a notion of Banach contractions that generalizes known results for Banach and local contractions. We apply the results obtained to an endogenous growth model and compare our approach with other well-known methods, such as the weighted contraction method, countable local contractions, and the Q-transform.