Compound vectors of subordinators and their associated positive Lévy copulas

Abstract

Levy copulas are an important tool which can be used to build dependent Levy processes. In a classical setting, they have been used to model financial applications. In a Bayesian framework they have been employed to introduce dependent nonparametric priors which allow to model heterogeneous data. This paper focuses on introducing a new class of Levy copulas based on a class of subordinators recently appeared in the literature, called Compound Random Measures. The well-known Clayton Levy copula is a special case of this new class. Furthermore, we provide some novel results about the underlying vector of subordinators such as a series representation and relevant moments. The article concludes with an application to a Danish fire dataset studied in Esmaeili and Kl\x7fuppelberg (2010).