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A Bellman approach to periodic optimization problems

Author

Listed:
  • Kvamsdal, Sturla F.

    (SNF – Centre for Applied Research)

  • Maroto, José M.

    (Dept. of Statistics and Operations Research II, Complutense University of Madrid)

  • Morán, Manuel

    (Dept. of Foundation of Economic Analysis I, Complutense University of Madrid)

  • Sandal, Leif K.

    (Dept. of Business and Management Science, Norwegian School of Economics)

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.

Suggested Citation

  • Kvamsdal, Sturla F. & Maroto, José M. & Morán, Manuel & Sandal, Leif K., 2016. "A Bellman approach to periodic optimization problems," Discussion Papers 2016/19, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2016_019
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    File URL: http://hdl.handle.net/11250/2423707
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    References listed on IDEAS

    as
    1. Ling Huang & Martin D. Smith, 2014. "The Dynamic Efficiency Costs of Common-Pool Resource Exploitation," American Economic Review, American Economic Association, vol. 104(12), pages 4071-4103, December.
    2. Kvamsdal, Sturla F. & Maroto, José M. & Morán, Manuel & Sandal, Leif K., 2020. "Bioeconomic modeling of seasonal fisheries," European Journal of Operational Research, Elsevier, vol. 281(2), pages 332-340.
    3. Martin D. Smith, 2012. "The New Fisheries Economics: Incentives Across Many Margins," Annual Review of Resource Economics, Annual Reviews, vol. 4(1), pages 379-402, August.
    4. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
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    Cited by:

    1. Ni, Yuanming & Sandal, Leif Kristoffer, 2019. "Seasonality matters: A multi-season, multi-state dynamic optimization in fisheries," European Journal of Operational Research, Elsevier, vol. 275(2), pages 648-658.

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    More about this item

    Keywords

    Bellman; optimization; periodicity; contraction operator; solution scheme;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery
    • Q57 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Ecological Economics

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