A Discrete Optimality System for an Optimal Harvesting Problem
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Date
2017
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Publisher
Springer Heidelberg
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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.
Description
Yılmaz, Fikriye/0000-0003-0002-9201; OZ BAKAN, HACER/0000-0001-8090-5552; Weber, Gerhard-Wilhelm/0000-0003-0849-7771
Keywords
Stochastic optimal control, Optimal harvesting, Stochastic partial differential equations, Symplectic partitioned Runge-Kutta schemes
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Citation
WoS Q
Scopus Q
Q3
Source
Volume
14
Issue
4
Start Page
519
End Page
533