年金与复利法则下的最优捕捞：逻辑斯蒂增长模型中的经济-生态权衡

中文摘要 AI 辅助

与物种增长特征相关的投资政策之间的关系，对于政策制定者寻求最合适的策略至关重要。在生态和经济背景下，平衡最大利润与物种可持续性始终是一个核心问题。本研究在最优控制的框架内，对年金和复利两种利息原则进行了比较分析。从资本理论的角度考察了各种投资政策，纳入了终值、累积函数和利息力等概念，这些概念均有助于制定最优控制策略。我们的分析基于包含线性捕捞的一维逻辑斯蒂模型。关键参数包括物种增长率和利率，并针对这些变量评估最优性。利用庞特里亚金最大值原理，我们推导了两种贴现法则下的最优捕捞政策，并刻画了由此产生的稳态均衡。主要发现表明，对于内在增长率低且年利率低的物种，年金利息法则能产生最优结果。相反，对于任何年利率，具有中等或较高增长率的物种在复利法则下能实现利润最大化。该研究还探讨了每种利息法则下不同增长率的最大净收入和最优策略。

英文摘要

The relationship between investment policy associated with species growth profile is essential in seeking the most appropriate strategy for a policymaker. Balancing maximum profit with the sustainability of species remains a central issue in both ecological and economic contexts. This study presents a comparative analysis of two interest principles, annuity and compounding, within the framework of optimal control. Various investment policies are examined from the perspective of capital theory, incorporating concepts such as future value, accumulation function, and force of interest, each contributing to the formulation of an optimal control strategy. Our analysis is based on a one dimensional logistic model incorporating linear harvesting. Key parameters include the species growth rate and interest rate, and optimality is evaluated with respect to these variables. Using Pontryagins Maximum Principle, we derive the optimal harvesting policies under both discounting laws and characterize the resulting steady state equilibria. The principal finding indicates that for species with low intrinsic growth rates and low annual interest rates, the annuity law of interest yields optimal outcomes. Conversely, for any annual interest rate, species exhibiting moderate or high growth rates maximize profit under the compound law of interest. The study also addresses maximum net revenue and optimal strategies for varying growth rates under each interest law.

发表机构

• Indian Statistical Institute（印度统计研究所）
• National Institute of Technology, Durgapur（杜尔加布尔国家技术学院）
• University of Calcutta（加尔各答大学）

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