This paper introduces $\textbf{gemact}$, a $\textbf{Python}$ package for actuarial modelling based on the collective risk model. The library supports applications to risk costing and risk transfer, loss aggregation, and loss reserving. We add new probability distributions to those available in $\textbf{scipy}$, including the (a, b, 0) and (a, b, 1) discrete distributions, copulas of the Archimedean family, the Gaussian, the Student t and the Fundamental copulas. We provide an implementation of the AEP algorithm for calculating the cumulative distribution function of the sum of dependent, non-negative random variables, given their dependency structure specified with a copula. The theoretical framework is introduced at the beginning of each section to give the reader with a sufficient understanding of the underlying actuarial models.

翻译：本文介绍基于集体风险模型的精算建模Python软件包$\textbf{gemact}$。该库支持风险定价与风险转移、损失聚合及损失准备金等应用场景。我们在$\textbf{scipy}$现有概率分布基础上新增了(a, b, 0)与(a, b, 1)离散分布族、阿基米德族连接函数、高斯连接函数、学生t连接函数及基本连接函数。针对给定依赖结构（由连接函数表征）的相依非负随机变量，我们实现了AEP算法以计算其和的累积分布函数。每节开篇引入理论框架，帮助读者充分理解底层精算模型。