RIEB, Kobe University

Existence and Uniqueness of a Fixed Point for the Bellman Operator in Deterministic Dynamic Programming

We study existence and uniqueness of a fixed point for the Bellman operator in deterministic dynamic programming. We show that removing many of the assumptions of the theorem on the Bellman operator recently shown by Martins-da-Rocha and Vailakis ("Existence and Uniqueness of a Fixed Point for Local Contractions," Econometrica 78, 1127-1141, 2010) does not affect its main conclusions concerning the existence and uniqueness of a fixed point. Under considerably weaker versions of the remaining assumptions, we also show that the value function can be computed by value iteration with an appropriate initial function.