Stochastic Differential Equations Harvesting Models

Nuno Brites (Lisbon School of Economics and Management)

Friday 11th April 11:00-12:00 Maths 311B

Abstract

In a fluctuating random environment, the dynamics of a fished population can be described by stochastic differential equations. We analyzed the profit performance of two policies: (1) an optimal policy with variable harvesting effort and (2) an optimal sustainable policy with constant effort. The former requires rapid changes in effort, making it impractical due to logistical and societal challenges. It also demands real-time population data, which is costly and imprecise. The sustainable strategy applies a constant effort, ensuring population stability and easing implementation. Using real data, we show that while the sustainable strategy yields slightly lower profits, it is more feasible. We also propose stepwise policies, where effort is adjusted annually or biennially, balancing practicality with profitability. Finally, we compare the profit margins of these approaches.

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