An Order-Theoretic Approach to Dynamic Programming: An Exposition
In this note, we discuss an order-theoretic approach to dynamic programming. In particular, we explain how order-theoretic fixed point theorems can be used to establish the existence of a fixed point of the Bellman operator, as well as why they are not sufficient to characterize the value function. By doing this, we present the logic behind the simple yet useful result recently obtained by Kamihigashi (2013) based on this order-theoretic approach.
Dynamic programming, Bellman equation, Value function, Fixed point
Research Institute for Economics and Business Administration
Rokkodai-cho, Nada-ku, Kobe