We formulate a stochastic impulse control model for animal population management and a candidate of exact solutions to a Hamilton–Jacobi–Bellman quasi-variational inequality. This model has a qualitatively different functional form of the performance index from the existing monotone ones. So far, optimality and unique solvability of the Hamilton–Jacobi–Bellman quasi-variational inequality has not been investigated, which are thus addressed in this paper. We present a candidate of exact solutions to the Hamilton–Jacobi–Bellman quasi-variational inequality and prove its optimality and unique solvability within a certain class of solutions in a viscosity sense. We also present and examine a dynamical system-based numerical method for computing coefficients in the exact solutions.

中文翻译：

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用于动物种群管理的Hamilton–Jacobi–Bellman拟变分不等式的精确粘度解

我们制定了用于动物种群管理的随机冲动控制模型，并提出了汉密尔顿-雅各比-贝尔曼准变分不等式的精确解的候选人。该模型的性能指标的功能形式与现有的单调模型不同。到目前为止，还没有研究汉密尔顿-雅各比-贝尔曼拟变分不等式的最优性和唯一可解性，因此本文将对此进行讨论。我们提出了一个针对Hamilton–Jacobi–Bellman拟变分不等式的精确解的候选人，并证明了它在特定类别的粘度意义上的最优性和独特的可溶性。我们还提出并研究了一种基于动态系统的数值方法，用于在精确解中计算系数。