Optimal Harvesting of a Fishery subject to Random Catastrophic Collapse

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.