In this paper we study the distributional properties of a vector of lifetimes modeled as the first arrival time between an idiosyncratic shock and a common systemic shock. Despite unlike the classical multidimensional Marshall-Olkin model here only a unique common shock affecting all the lifetimes is assumed, some dependence is allowed between each idiosyncratic shock arrival time and the systemic one. The dependence structure of the resulting distribution is studied through the analysis of its singularity, its associated survival copula function and conditional hazard rates. Finally, some possible applications to actuarial and credit risk financial products are proposed.

在本文中，我们研究了寿命向量的分布特性，该向量被建模为特殊冲击和普通系统冲击之间的首次到达时间。尽管与经典的多维 Marshall-Olkin 模型不同，这里只假设了一个影响所有生命周期的独特的共同冲击，但在每个特殊冲击到达时间和系统性冲击到达时间之间允许有一些依赖性。通过分析其奇异性、相关的生存 copula 函数和条件风险率来研究所得分布的依赖结构。最后，提出了精算和信用风险金融产品的一些可能应用。