Optimal harvesting under uncertain environment with clusters of catastrophes

The fishery industry is facing increasing challenges in the exploitation of marine resources. Marine resources are classic examples of common-property resources subject to fundamental problems of economic waste and over-exploitation, which may lead to resource destruction, including extinction. The past decades have highlighted the relevance of ecological catastrophes, such as the fate of the cod population in the Northwest Atlantic. These events do not occur with a constant frequency, but are clustered over time. Our objective is to study a harvesting management problem under the assumption that unexpected ecological disasters may occur in clusters. We model this clustering phenomenon using marked Hawkes processes. We characterize our value function as the unique solution to a Hamilton-Jacobi-Bellman inequality. We describe the optimal harvesting strategy by identifying the harvesting and non-harvesting regions. Our results are counterintuitive, challenging the generally accepted belief that, when facing an increasing risk of decimation due to disasters, the optimal harvesting policy should lead to a reduction in harvesting activity. These findings offer valuable insights into the fragile nature of fish resources, potentially explaining the collapse of fisheries in the Northwest Atlantic. Governments and international authorities must take action against the causes of such disasters, such as pollution and the overexploitation of marine resources, in order to reduce the risk of further decimation and to better assess and address the true cost of marine resource extinction. We further enrich our study with numerical analysis, providing additional insights into the optimal harvesting policy.