On the option interpretation of rational harvesting planning

We consider the determination of the harvesting strategy maximizing the present expected value of the cumulative yield from the present up to extinction. By relying on a combination of stochastic calculus, ordinary nonlinear programming, and the classical theory of diffusions, we show that if the underlying population evolves according to a logistic diffusion subject to a general diffusion coefficient, then there is a single threshold density at which harvesting should be initiated in a singular fashion. We derive the condition which uniquely determines the threshold and show that harvesting should be initiated only when the option value of further preserving another individual falls below its opportunity cost. In this way, we present a real option interpretation of rational harvesting planning. We also consider the comparative static properties of the value of the harvesting opportunity and state a set of usually satisfied conditions under which increased stochastic fluctuations (demographic or environmental) decrease the expected cumulative yield from harvesting and increase the optimal harvesting threshold, thus postponing the rational exercise of the irreversible harvesting decision.