Multiple risk factor dependence structures: Distributional properties

Abstract

We introduce a class of dependence structures, that we call the Multiple Risk Factor (MRF) dependence structures. On the one hand, the new constructions extend the popular CreditRisk approach, and as such they formally describe default risk portfolios exposed to an arbitrary number of fatal risk factors with conditionally exponential and dependent hitting (or occurrence) times. On the other hand, the MRF structures can be seen as an encompassing family of multivariate probability distributions with univariate margins distributed Pareto of the 2nd kind, and in this role they can be used to model insurance risk portfolios of dependent and heavy tailed risk components.

Keywords: Multivariate distributions, dependence, singularity, Pareto distributions, credit risk, factor models, weighted risk functionals