Compound vectors of subordinators and their associated positive L\'evy copulas

TL;DR

This paper introduces a new class of Le9vy copulas derived from compound subordinators, expanding modeling capabilities for dependent processes, with theoretical insights and an application to fire data.

Contribution

It presents a novel class of Le9vy copulas based on compound subordinators, including theoretical properties and an application to real-world data.

Findings

New class of Le9vy copulas based on compound subordinators

Series representation and moments of the underlying vector

Application to Danish fire dataset

Abstract

L\'evy copulas are an important tool which can be used to build dependent L\'evy 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 L\'evy copulas based on a class of subordinators recently appeared in the literature, called \textit{Compound Random Measures}. The well-known Clayton L\'evy 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.