Deterministic Discrete Dynamic Programming with Discount Factor Greater than One: Structure of Optimal Policies

The paper considers the deterministic dynamic programming model with discount factor greater than one. Possible applications are discussed. After the introduction of a suitable optimization criterion, it is shown that stationary policies are not necessarily optimal and that optimal finite horizon policies do not necessarily converge to an optimal infinite horizon policy. These difficulties are circumvented by the use of a special method, called asymptotic analysis, that allows for inductive arguments on finite horizon models. Asymptotic analysis yields the structure of optimal policies. An optimal policy will usually belong to a special class of history remembering policies.