A Bellman Approach to Periodic Optimization Problems

15 Pages Posted: 1 Dec 2016

See all articles by Sturla Kvamsdal

Sturla Kvamsdal

Norwegian School of Economics (NHH)

Jose M. Maroto

Universidad Complutense de Madrid (UCM)

Manuel Moran

Universidad Complutense de Madrid (UCM)

Leif Kristoffer Sandal

Norwegian School of Economics (NHH) - Department of Business and Management Science

Date Written: November 25, 2016

Abstract

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

Kvamsdal, Sturla and Maroto, Jose M. and Moran, Manuel and Sandal, Leif Kristoffer, A Bellman Approach to Periodic Optimization Problems (November 25, 2016). NHH Dept. of Business and Management Science Discussion Paper No. 2016/19, Available at SSRN: https://ssrn.com/abstract=2877764 or http://dx.doi.org/10.2139/ssrn.2877764

Sturla Kvamsdal (Contact Author)

Norwegian School of Economics (NHH) ( email )

Helleveien 30
Bergen, NO-5045
Norway

Jose M. Maroto

Universidad Complutense de Madrid (UCM) ( email )

Carretera de Humera s/n
Madrid, Madrid 28223
Spain

HOME PAGE: http://www.ucm.es/info/eiop/profesores.php?id=maroto

Manuel Moran

Universidad Complutense de Madrid (UCM) ( email )

Carretera de Humera s/n
Madrid, Madrid 28223
Spain

HOME PAGE: http://www.ucm.es/info/anaeco/html/manuel.htm

Leif Kristoffer Sandal

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway
+47 55 95 93 41 (Phone)

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