Optimal harvesting under stochastic fluctuations and critical depensation

We consider the derivation of the optimal harvesting strategy maximizing the expected cumulative yield from present up to extinction, under the assumption that the harvested population fluctuates stochastically and is subjected to an Allee-effect. By relying on both stochastic calculus and the classical theory of linear diffusions, we derive both the optimal harvesting thresholds at which harvesting should be initiated at full capacity and the value of the optimal strategy. In contrast to ordinary models which are absent of critical depensation, we show that the presence of an Allee-effect leads to the introduction of a lower harvesting threshold at which the population should be immediately depleted under the optimal policy. Moreover, we demonstrate that discounting increases the incentives to harvest and, therefore, increases the probability of a soon extinction of the harvested population.