The conservation and exploitation of vulnerable resources |
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Authors: | William J Reed Hector Echavarría Heras |
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Institution: | (1) Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, V8W 3P4 Victoria, British Columbia, Canada;(2) Centro de Investigación Científica y de Educación, Superior de Ensenada, Ensenada, Mexico |
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Abstract: | The maximum principle of deterministic optimal control, which has proved to be a very useful tool in theoretical bioeconomics,
is extended in this article to cover the optimal exploitation of a biological resource vulnerable to catastrophic collapse,
the probability of which may depend in general on the state of the resource, the current control and time. A general formulation
of the maximum principle for such stochastic problems is presented and a number of applications are outlined. These include:
optimal harvesting of a fishery vulnerable to catastrophic collapse; optimal thinning of a forest vulnerable to fire; optimal
expenditure and investment in forest fire protection and optimal consumption-pollution tradeoffs in an ecosystem vulnerable
to pollution-related collapse. In addition an application of the method to a highly stylized behavioral ecology model is given. |
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