Optimal harvesting from interacting populations in a stochastic environment

Journal article

Authors/Editors

Lungu, Edward

Research Areas

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Publication Details

Author list: Lungu E, Oksendal B

Publisher: Bernoulli Society for Mathematical Statistics and Probability

Place: VOORBURG

Publication year: 2001

Journal acronym: BERNOULLI

Volume number: 7

Issue number: 3

Start page: 527

End page: 539

Number of pages: 13

ISSN: 1350-7265

Languages: English-Great Britain (EN-GB)

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Abstract

Consider n populations whose sizes are given by stochastic differential equations driven by m-dimensional Brownian motion. We study the following problem: what harvesting strategy from the n populations maximizes the expected total income from the harvest? We formulate this as a (singular) stochastic control problem and give sufficient conditions for the existence of an optimal strategy. Our results lead to the one-at-a-time principle that it is almost surely never optimal to harvest from more than one population at a time.

Keywords

one-at-a-time principle, optimal harvesting, singular stochastic control, stochastic systems, variational inequalities, verification theorem

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