Harvesting optimization with stochastic differential equations models: is the optimal enemy of the good?

Abstract

We can describe the size evolution of a harvested population in a randomly varying environment using stochastic differential equations. Previously, we have compared the profit performance of four harvesting policies: (i) optimal variable effort policy, based on variable effort; (ii) optimal penalized variable effort policies, penalized versions based on including an artificial running energy cost on the effort; (iii) stepwise policies, staircase versions where the harvesting effort is determined at the beginning of each year (or of each biennium) and kept constant throughout that year (or biennium); (iv) constant harvesting effort sustainable policy, based on constant effort. They have different properties, so it is also worth looking at combinations of such policies and studying the single and cross-effects of the amount of penalization, the absence or presence and type of steps, and the restraints on minimum and maximum allowed efforts. Using data based on a real harvested population and considering a logistic growth model, we perform such a comparison study of pure and mixed policies in terms of profit, applicability, and other relevant properties. We end up answering the question: is the optimal enemy of the good?