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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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