Optimal harvesting of stochastically fluctuating populations

摘要: We obtain the optimal harvesting plan to maximize expected discounted number of individuals harvested over an infinite future horizon, under most common (Verhulst-Pearl) logistic model for a stochastically fluctuating population. also solve problem standard variants where there are constraints on admissible rates. use stochastic calculus derive population threshold at which as well overall value in sense model. show that except extreme conditions, is never depleted finite time, but remains stationary distribution we find explicitly. Needless say, our results prove any strategy totally depletes sub-optimal. These much more precise than those previously obtained this problem.