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.
Dynamic programming, Bellman operator, value function, fixed point.
RIEB, Kobe University
Rokkodai-cho, Nada-ku, Kobe