A logistic type stochastic control model for cost-effective single-species population management subject to an ambiguous jump intensity is presented based on the modern multiplier-robust formulation. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation for finding the optimal control is then derived. Mathematical analysis of the HJBI equation from the viewpoint of viscosity solutions is carried out with an emphasis on the non-linear and non-local term, which is a key term arising due to the jump ambiguity. We show that this term can be efficiently handled in the framework of viscosity solutions by utilizing its monotonicity property. A numerical scheme to discretize the HJBI equation is presented as well. Our model is finally applied to management of algae population in river environment. Optimal management policies ranging from the short-term to long-term viewpoints are numerically investigated.

提出了一种基于现代乘数稳健公式的逻辑型随机控制模型，用于在不明确的跳跃强度下进行具有成本效益的单物种种群管理。然后导出用于寻找最优控制的 Hamilton-Jacobi-Bellman-Isaacs (HJBI) 方程。从粘度解的角度对HJBI方程进行数学分析，重点是非线性和非局部项，这是由于跳跃歧义而产生的关键项。我们表明，通过利用其单调性，可以在粘度解决方案的框架中有效地处理该术语。还提出了离散化 HJBI 方程的数值方案。我们的模型最终应用于河流环境中藻类种群的管理。