Lévy Copulas: Review of Recent Results.

Summary We review and extend the now considerable literature on Levy copulas. First, we focus on Monte Carlo methods and present a new robust algorithm for the simulation of multidimensional Levy processes with dependence given by a Levy copula. Next, we review statistical estimation techniques in a parametric and a non-parametric setting. Finally, we discuss the interplay between Levy copulas and multivariate regular variation and briefly review the applications of Levy copulas in risk management. In particular, we provide a new easy-to-use sufficient condition for multivariate regular variation of Levy measures in terms of their Levy copulas.