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Mathematical Medicine and Biology 1988 5(3):215-235; doi:10.1093/imammb/5.3.215
© 1988 by Institute of Mathematics and its Applications
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Optimal Harvesting of a Fishery subject to Random Catastrophic Collapse

WILLIAM J. REED

Department of Mathematics, University of Victoria PO Box 1700, Victoria British Columbia, Canada V8W 2Y2

The socially optimal harvesting policy for a fishery subject to random catastrophic collapse is determined. It is shown how the problem can be converted to one of deterministic optimal control and a solution obtained using the Pontryagin maximum principle. The optimal stock biomass satisfies a golden-independent effects of the risk of collapse. These effects have opposite influences on the optimal biomass level. The optimal policy when there is the possibility of a recovery after a collapse is discussed. Economic interpretations of the results are given, and some numerical results presented.


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