Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2016/19: A Bellman approach to periodic optimization problems

Sturla F. Kvamsdal (), José M. Maroto (), Manuel Morán () and Leif K. Sandal ()
Additional contact information
Sturla F. Kvamsdal: SNF – Centre for Applied Research, Postal: SNF – Centre for Applied Research, Helleveien 30, N-5045 Bergen, Norway
José M. Maroto: Dept. of Statistics and Operations Research II, Complutense University of Madrid, Postal: Complutense University of Madrid , Department of Statistics and Operations Research II, 28223 Madrid, Spain
Manuel Morán: Dept. of Foundation of Economic Analysis I, Complutense University of Madrid, Postal: Complutense University of Madrid , Department of Foundation of Economic Analysis I, 28223 Madrid, Spain
Leif K. Sandal: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway

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-codes: C61; Q22; Q57

14 pages, November 30, 2016

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