标题： 在随机环境中关于最优收获：松弛模型中的最优策略 显示英文标题

标题： On Optimal Harvesting in Stochastic Environments: Optimal Policies in a Relaxed Model

摘要： 本文考察了在随机环境中最优捕获单一物种的目标。Alvarez（2000）曾使用动态规划技术分析过此问题，但由于价格速率函数的自然收益结构（即种群数量增加时价格下降），不存在最优捕获策略。本文以一种松弛的形式建立了捕获模型，使得不仅能够证明存在最优的松弛捕获策略，还可以识别它。该分析将捕获问题嵌入到一个无限维线性规划问题中，其中初始位置作为参数进入，并随后分析一个具有较少约束条件的辅助问题。通过这种方式，确定了最优值（给定初始位置）的上界；这些上界取决于初始种群规模与特定目标规模之间的关系。更有趣的情况出现在初始种群规模超过该目标规模时；需要一个新的论证来获得精确的上界。尽管初始种群规模仅作为一个参数进入，但其值由该参数的闭式函数表达式决定。 显示英文摘要

摘要： This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in Alvarez (2000) using dynamic programming techniques and, due to the natural payoff structure of the price rate function (the price decreases as the population increases), no optimal harvesting policy exists. This paper establishes a relaxed formulation of the harvesting model in such a manner that existence of an optimal relaxed harvesting policy can not only be proven but also identified. The analysis embeds the harvesting problem in an infinite-dimensional linear program over a space of occupation measures in which the initial position enters as a parameter and then analyzes an auxiliary problem having fewer constraints. In this manner upper bounds are determined for the optimal value (with the given initial position); these bounds depend on the relation of the initial population size to a specific target size. The more interesting case occurs when the initial population exceeds this target size; a new argument is required to obtain a sharp upper bound. Though the initial population size only enters as a parameter, the value is determined in a closed-form functional expression of this parameter.