Optimal harvesting from a population in a stochastic crowded environment

E. M. Lungu, B. Øksendal

Research output: Contribution to journalArticle

87 Citations (Scopus)

Abstract

We study the (Ito) stochastic differential equation dX(t) = rX(t)(K - X(t))dt + aX(t)(K - X(t))dB(t), X0 = x > 0 as a model for population growth in a stochastic environment with finite carrying capacity K > 0. Here r and a are constants and B(t) denotes Brownian motion. If r ≤ 0, we show that this equation has a unique strong global solution for all x > 0 and we study some of its properties. Then we consider the following problem: What harvesting strategy maximizes the expected total discounted amount harvested (integrated over all future times)? We formulate this as a stochastic control problem. Then we show that there exists a constant optimal 'harvest trigger value' x* ε (0, K) such that the optimal strategy is to do nothing if X(t) < x* and to harvest X(t) - x* if X(t) > x*. This leads to an optimal population process X(t) being reflected downward at x*. We find x* explicitly.

Original languageEnglish
Pages (from-to)47-75
Number of pages29
JournalMathematical Biosciences
Volume145
Issue number1
DOIs
Publication statusPublished - Oct 1 1997

Fingerprint

Optimal Harvesting
Optimal Constants
Finite Capacity
Carrying Capacity
Population Growth
Brownian movement
Stochastic Control
Conservation of Natural Resources
Harvesting
Optimal Strategy
Trigger
Global Solution
Stochastic Equations
Brownian motion
Control Problem
Differential equations
Maximise
Differential equation
Denote
carrying capacity

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Cite this

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Optimal harvesting from a population in a stochastic crowded environment. / Lungu, E. M.; Øksendal, B.

In: Mathematical Biosciences, Vol. 145, No. 1, 01.10.1997, p. 47-75.

Research output: Contribution to journalArticle

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AU - Øksendal, B.

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