A discrete optimality system for an optimal harvesting problem

Hacer Öz Bakan (), Fikriye Yılmaz () and Gerhard-Wilhelm Weber ()
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Hacer Öz Bakan: Atılım University
Fikriye Yılmaz: Gazi University
Gerhard-Wilhelm Weber: Middle East Technical University

Computational Management Science, 2017, vol. 14, issue 4, No 4, 519-533

Abstract: 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.

Keywords: Stochastic optimal control; Optimal harvesting; Stochastic partial differential equations; Symplectic partitioned Runge–Kutta schemes (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10287-017-0286-5

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