In this paper, we explore the use of an extensive list of Archimedean copulas in general and life insurance modelling. We consider not only the usual choices like the Clayton, Gumbel–Hougaard, and Frank copulas but also several others which have not drawn much attention in previous applications. First, we apply different copula functions to two general insurance data sets, co-modelling losses and allocated loss adjustment expenses, and also losses to building and contents. Second, we adopt these copulas for modelling the mortality trends of two neighbouring countries and calculate the market price of a mortality bond. Our results clearly show that the diversity of Archimedean copula structures gives much flexibility for modelling different kinds of data sets and that the copula and tail dependence assumption can have a significant impact on pricing and valuation. Moreover, we conduct a large simulation exercise to investigate further the caveats in copula selection. Finally, we examine a number of other estimation methods which have not been tested in previous insurance applications.

中文翻译：

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关于使用阿基米德联结进行保险建模

在本文中，我们探讨了在一般和人寿保险建模中使用广泛的阿基米德 copula 列表。我们不仅考虑了 Clayton、Gumbel-Hougaard 和 Frank copula 等常用选择，还考虑了其​​他几个在以前的应用中没有引起太多关注的选择。首先，我们将不同的 copula 函数应用于两个通用保险数据集，即联合建模损失和分配的损失调整费用，以及建筑物和内容的损失。其次，我们采用这些 copula 对两个邻国的死亡率趋势进行建模，并计算死亡率债券的市场价格。我们的结果清楚地表明，阿基米德 copula 结构的多样性为建模不同类型的数据集提供了很大的灵活性，并且 copula 和尾部依赖假设可以对定价和估值产生重大影响。此外，我们进行了一次大型模拟练习，以进一步研究 copula 选择中的注意事项。最后，我们研究了一些其他的估计方法，这些方法在以前的保险应用中没有经过测试。