Harvesting from a Population in a Stochastic Crowded Environment with Harvesting Cost

摘要

We study the problem on optimal harvesting from a population in a stochastic crowded environment with harvesting cost. In this problem, the size of the population satisfy the stochastic logistic differential equation, which serves as a model for population growth in a stochastic environment with finite carrying capacity when harvesting is exercised. We consider the following problem: What harvesting strategy maximizes the expected discounted total harvested profit? We formulate this as a stochastic control problem and obtain the optimal harvesting strategy and the corresponding optimal harvesting profit function explicitly.