In this paper we show how to extend a simple common shock model with Archimedean dependence of the hidden variables to the non-exchangeable case. The assumption is that the hidden risk factors are linked by a hierarchical Archimedean dependence structure, possibly fully nested. We give directions about how to implement the model and to address the issue that the hidden variables must be put in descending dependence order. We show how the model can be simplified in the Gumbel-Marshall-Olkin distribution in Cherubini and Mulinacci (2017), the only case in which exponential distribution of the observed variables is preserved.

中文翻译：

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常见冲击模型中的分层Archimedean依赖

在本文中，我们展示了如何将具有隐藏变量的阿基米德依赖性的简单通用冲击模型扩展到不可交换的情况。假定隐藏的风险因素由分层的阿基米德依赖结构（可能完全嵌套）链接在一起。我们给出了有关如何实现模型以及解决必须将隐式变量按降序依存关系放置的问题的指导。我们展示了如何在Cherubini和Mulinacci（2017）的Gumbel-Marshall-Olkin分布中简化模型，这是唯一保留观测变量指数分布的情况。