论文标题
右截断的Archimedean和相关的Copulas
Right-truncated Archimedean and related copulas
论文作者
论文摘要
考虑了从右侧截断的标准均匀单变量边缘的随机向量的Copulas，并得出了这种右截断的条件性copulas的一般公式。该公式对Copulas进行了分析，可以分析作为每个参数的函数。例如，对于Archimedean和相关的Copulas就是这种情况。由此产生的右截断的Archimedean Copulas不仅可以在分析上拖延，而且还可以被描述为倾斜的Archimedean Copulas。例如，这一发现使人们可以更容易地得出分析性能，例如尾部依赖性的系数或右截断的阿基米斯copulas的采样程序。另一个结果，可以轻松获得限制性的克莱顿副群，以使截断点的一般向量融合到零。这是（重新）保险的重要财产，也是在同等截断点的特殊情况下已经知道的事实，但很难没有上述表征。此外，带有逻辑稳定尾部依赖功能的右截断的Archimax Copulas的特征是倾斜的外部功率Archimedean Copulas，并且还得出了右置嵌套的Archimedean Copulas的分析形式。
The copulas of random vectors with standard uniform univariate margins truncated from the right are considered and a general formula for such right-truncated conditional copulas is derived. This formula is analytical for copulas that can be inverted analytically as functions of each single argument. This is the case, for example, for Archimedean and related copulas. The resulting right-truncated Archimedean copulas are not only analytically tractable but can also be characterized as tilted Archimedean copulas. This finding allows one, for example, to more easily derive analytical properties such as the coefficients of tail dependence or sampling procedures of right-truncated Archimedean copulas. As another result, one can easily obtain a limiting Clayton copula for a general vector of truncation points converging to zero; this is an important property for (re)insurance and a fact already known in the special case of equal truncation points, but harder to prove without aforementioned characterization. Furthermore, right-truncated Archimax copulas with logistic stable tail dependence functions are characterized as tilted outer power Archimedean copulas and an analytical form of right-truncated nested Archimedean copulas is also derived.
