A discrete optimality system for an optimal harvesting problem


Bakan H. O. , YILMAZ F. N. , Weber G.

COMPUTATIONAL MANAGEMENT SCIENCE, vol.14, no.4, pp.519-533, 2017 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.1007/s10287-017-0286-5
  • Title of Journal : COMPUTATIONAL MANAGEMENT SCIENCE
  • Page Numbers: pp.519-533

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.