Existence and uniqueness of solutions to the Bellman equation in stochastic dynamic programming
Articles
Overview
published in
- Theoretical Economics Journal
publication date
- July 2024
issue
- 3
volume
- 19
Digital Object Identifier (DOI)
International Standard Serial Number (ISSN)
- 1933-6837
Electronic International Standard Serial Number (EISSN)
- 1555-7561
abstract
- 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.
Classification
keywords
- bellman equation; c61; contraction mapping; e21; endogenous growth; local contraction; q-transform; stochastic dynamic programming; weighted contraction