Optimal Harvesting of a Stochastic Logistic Model Driven by One-Sided Tempered Stable Process

TL;DR

This paper analyzes a stochastic logistic harvesting model driven by tempered stable processes, establishing conditions for population outcomes, deriving optimal strategies, and examining the influence of process parameters through simulations.

Contribution

It introduces explicit solutions for optimal harvesting and maximum sustainable yield in a model driven by one-sided tempered stable processes, highlighting the effects of key parameters.

Findings

Threshold conditions for extinction and persistence are established.

Explicit solutions for optimal harvesting effort are derived.

Parameter effects on strategies are systematically analyzed.

Abstract

This paper investigates a class of stochastic Logistic harvesting models driven by tempered stable processes, with a one-sided power-law L\'evy measure. We establish threshold conditions for population extinction and persistence, prove the distributional stability of the model, and derive explicit solutions for the optimal harvesting effort and the maximum sustainable yield. We systematically analyze the effects of white noise intensity and L\'evy jump intensity on the optimal harvesting strategy. In particular, by focusing on the intrinsic structural parameters of the L\'evy measure, namely the stability index and the tempering parameter, we elucidate their roles in shaping the optimal strategy and propose four targeted intervention strategies. Numerical simulations are presented to validate the theoretical findings.