A Marshall-Olkin Type Multivariate Model with Underlying Dependent Shocks

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 afecting 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.