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. Without any topo- logical assumption, we show that the Bellman operator has a unique fixed point in a restricted domain, that this fixed point is the value function, and that the value function can be computed by value iter-ation.
Dynamic programming, Bellman operator, Value function, Fixed point
Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan
Rokkodai-cho, Nada-ku, Kobe