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

publication date

  • July 2024

start page

  • 1223

end page

  • 1260

issue

  • 3

volume

  • 19

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.

subjects

  • Economics

keywords

  • stochastic dynamic programming; bellman equation; contraction mapping; weighted contraction; local contraction; q-transform; endogenous growth; c61; e20