Lévy Processes and Lévy Copulas

This thesis discusses Lévy processes and Lévy copulas. In connection with Lévy processes we treat some of the theory behind infinitely divisible distributions, acknowledging that the two classes are equivalent.Within the class of Lévy processes we will mostly look at stable processes and compound Poisson processes. The theory of Lévy processes dates back to the late 1920s, after de Finetti first introduced the class of infinitely divisible distributions. Since then Lévy processes have become popular tools for modelling in finance, insurance and physics. Lévy copulas were introduced by Peter Tankov in 2003 in order to model dependency between different components of a multivariate Lévy process. In the last part of the book we present an application of Lévy copulas in non-life insurance and ruin theory of a Lévy copula. Through this example we will discuss aspects regarding estimation of the parameters and goodness of fit.