Existence and uniqueness of solutions to the Bellman equation in stochastic dynamic programming
建立了一个分析离散时间随机动态优化问题的框架，通过推广巴拿赫压缩概念，得到了贝尔曼方程解的存在性和唯一性新结果，并应用于内生增长模型。
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.