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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.

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