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Optimal harvesting of a fishery subject to random catastrophic collapse. (English) Zbl 0657.90032
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-rule equation containing extra terms reflecting the density-dependent and density-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.

MSC:
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
91B62 Economic growth models
93E20 Optimal stochastic control
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