Optimal harvesting under marine reserves and uncertain environment

Persistence in the literature is the perception of an inherent tradeoff between ecological conservation and economic harvesting goals. Overexploitation may lead to resource destruction, including extinction. Conservation measures should be decided and implemented. A standard ecological response is to impose no-take areas or marine reserves. In this paper, our objective is to study a harvesting management problem under the constraints of a no-take area, which we formulate mathematically as a bi-dimensional singular stochastic control problem. Using dynamic programming theory, we characterise our value function as the unique solution to a HJB equation. We also describe the optimal harvesting strategy by identifying the harvesting and non-harvesting regions. We show that setting up reserve area not only leads to a better ecological conservation but may also increase the economic benefit for fishing industry in the long run. We further enrich our studies with some numerical analysis, enabling us to get some insightful understanding on the size of the reserve area where no-take policy should be implemented.