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A discrete optimality system for an optimal harvesting problem

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Abstract

In this paper, we obtain the discrete optimality system of an optimal harvesting problem. While maximizing a combination of the total expected utility of the consumption and of the terminal size of a population, as a dynamic constraint, we assume that the density of the population is modeled by a stochastic quasi-linear heat equation. Finite-difference and symplectic partitioned Runge–Kutta (SPRK) schemes are used for space and time discretizations, respectively. It is the first time that a SPRK scheme is employed for the optimal control of stochastic partial differential equations. Monte-Carlo simulation is applied to handle expectation appearing in the cost functional. We present our results together with a numerical example. The paper ends with a conclusion and an outlook to future studies, on further research questions and applications.

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Authors and Affiliations

  1. Department of Mathematics, Atılım University, 06836, Ankara, Turkey

    Hacer Öz Bakan

  2. Department of Mathematics, Gazi University, 06500, Ankara, Turkey

    Fikriye Yılmaz

  3. Institute of Applied Mathematics, Middle East Technical University, 06800, Ankara, Turkey

    Gerhard-Wilhelm Weber

Authors
  1. Hacer Öz Bakan
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  2. Fikriye Yılmaz
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  3. Gerhard-Wilhelm Weber
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Correspondence to Hacer Öz Bakan.

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Öz Bakan, H., Yılmaz, F. & Weber, GW. A discrete optimality system for an optimal harvesting problem. Comput Manag Sci 14, 519–533 (2017). https://doi.org/10.1007/s10287-017-0286-5

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  • DOI: https://doi.org/10.1007/s10287-017-0286-5

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