A Bellman Approach to Periodic Optimization Problems
15 Pages Posted: 1 Dec 2016
Date Written: November 25, 2016
We consider an infinite horizon optimization problem with arbitrary but finite periodicity in discrete time. The problem can be formulated as a fix-point problem for a contraction operator, and we provide a solution scheme for this class of problems. Our approach is an extension of the classical Bellman problem to the special case of non-autonomy that periodicity represents. Solving such problems paves the way for consistent and rigorous treatment of, for example, seasonality in discrete dynamic optimization. In an illustrative example, we consider the decision problem in a fishery with seasonal fluctuations. The example demonstrates that rigorous treatment of periodicity has profound influence on the optimal policy dynamics compared to the case where seasonality is abstracted from by considering average effects only.
Keywords: Bellman, optimization, periodicity, contraction operator, solution scheme
JEL Classification: C61, Q22, Q57
Suggested Citation: Suggested Citation