随机环境中种群的最优可持续收获
Optimal sustainable harvesting of populations in random environments
摘要：
我们研究的最佳可持续收获的人口，生活在一个随机的环境。我们设置的新颖之处在于，我们最大限度地提高了渐近收获产量，无论是在期望值和几乎必然的意义上，为一大类收获策略和非结构化的人口模型。我们证明了相对较弱的假设下，存在一个唯一的最优收获策略，其特征在于一个最优阈值，低于该阈值的人口是保持在所有时间利用当地时间推型政策。我们还讨论了，通过阿贝尔极限，我们的结果是如何相关的最优收获策略时，最大化的收获产量的预期累积现值，并建立一个简单的连接和排序之间的值和最优边界。最后，我们明确地描述了两种不同情况下的最优收获策略，其中之一是著名的随机Verhulst Pearl Logistic模型的人口增长。
英文摘要：
We study the optimal sustainable harvesting of a population that lives in a random environment. The novelty of our setting is that we maximize the asymptotic harvesting yield, both in an expected value and almost sure sense, for a large class of harvesting strategies and unstructured population models. We prove under relatively weak assumptions that there exists a unique optimal harvesting strategy characterized by an optimal threshold below which the population is maintained at all times by utilizing a local time push-type policy. We also discuss, through Abelian limits, how our results are related to the optimal harvesting strategies when one maximizes the expected cumulative present value of the harvesting yield and establish a simple connection and ordering between the values and optimal boundaries. Finally, we explicitly characterize the optimal harvesting strategies in two different cases, one of which is the celebrated stochastic Verhulst Pearl logistic model of population growth.
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