带收获配额的随机种群资源提取问题
Resource Extraction from a Stochastic Population with Harvesting Quotas
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中文总结 AI 辅助
针对带收获配额的随机种群资源提取问题，研究最优收获策略的阈值条件，证明最优阈值可为0，并建立收获率趋于无穷时奇异控制问题解的收敛性。
中文摘要 AI 辅助
我们研究遍历型的资源提取问题，其中收获配额作为当前生物量的函数对收获率加以限制。在扩散动力学设定下，我们给出最优收获策略为阈值型的条件。与采用奇异控制的无约束情形不同，最优阈值可为0，对应始终以最大可能速率收获。此外，我们证明了当收获率趋于无穷时，对应奇异控制问题的解会收敛。
英文摘要
We study a resource extraction problem of ergodic type, where harvesting quotas are imposed that restrict the harvesting rate by a function of the current biomass. In a setting with diffusive dynamics, we provide conditions under which the optimal harvesting strategy is of threshold type. In contrast with the unrestricted case with singular controls, the optimal threshold may be 0, which corresponds to harvesting at the maximal possible rate at all times. Furthermore, we establish the convergence of the solution to the corresponding singular control problem as the harvesting rate tends to infinity.
