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Numerical computation of the optimal vector field: Exemplified by a fishery model

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  • Grass, D.
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    Abstract

    Numerous optimal control models analyzed in economics are formulated as discounted infinite time horizon problems, where the defining functions are nonlinear as well in the states as in the controls. As a consequence solutions can often only be found numerically. Moreover, the long run optimal solutions are mostly limit sets like equilibria or limit cycles. Using these specific solutions a BVP approach together with a continuation technique is used to calculate the parameter dependent dynamic structure of the optimal vector field. We use a one dimensional optimal control model of a fishery to exemplify the numerical techniques. But these methods are applicable to a much wider class of optimal control problems with a moderate number of state and control variables.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0165188912000966
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 36 (2012)
    Issue (Month): 10 ()
    Pages: 1626-1658

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    Handle: RePEc:eee:dyncon:v:36:y:2012:i:10:p:1626-1658

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    Web page: http://www.elsevier.com/locate/jedc

    Related research

    Keywords: Optimal vector field; BVP; Continuation; Multiple optimal solutions; Threshold point;

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    References

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    1. Kiseleva, T. & Wagener, F.O.O., 2011. "Bifurcations of Optimal Vector Fields," CeNDEF Working Papers 11-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    2. Levy, Amnon & Neri, Frank & Grass, Dieter, 2006. "Macroeconomic Aspects Of Substance Abuse: Diffusion, Productivity And Optimal Control," Macroeconomic Dynamics, Cambridge University Press, vol. 10(02), pages 145-164, April.
    3. Peter Kunkel & Oskar von dem Hagen, 2000. "Numerical Solution of Infinite-Horizon Optimal-Control Problems," Computational Economics, Society for Computational Economics, vol. 16(3), pages 189-205, December.
    4. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-72, March.
    5. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
    6. Michel, P., 1980. "On the Transversality Condition in Infinite Horizon Optimal Problems," Cahiers de recherche 8024, Universite de Montreal, Departement de sciences economiques.
    7. Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Hartl, Richard F. & Kort, Peter M., 2011. "Two state capital accumulation with heterogenous products: Disruptive vs. non-disruptive goods," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 462-478, April.
    8. Hartl, Richard F., 1987. "A simple proof of the monotonicity of the state trajectories in autonomous control problems," Journal of Economic Theory, Elsevier, vol. 41(1), pages 211-215, February.
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    Cited by:
    1. Florian Wagener, 2013. "Shallow lake economics run deep: nonlinear aspects of an economic-ecological interest conflict," Computational Management Science, Springer, vol. 10(4), pages 423-450, December.

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