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.
@article{1080004764,
author = {Lungu, Edward and \o ksendal, Bernt},
title = {Optimal harvesting from interacting populations in a stochastic environment},
journal = {Bernoulli},
volume = {7},
number = {6},
year = {2001},
pages = { 527-539},
language = {en},
url = {http://dml.mathdoc.fr/item/1080004764}
}
Lungu, Edward; øksendal, Bernt. Optimal harvesting from interacting populations in a stochastic environment. Bernoulli, Tome 7 (2001) no. 6, pp. 527-539. http://gdmltest.u-ga.fr/item/1080004764/