Claudia Kluppelberg and Sidney Resnick

The copula of a multivariate distribution is the distribution transformed to have uniform one dimensional marginals. We review a transformation of the marginals of a multivariate distribution to a standard Pareto and the resulting distribution we call the Pareto copula. Use of the Pareto copula has a certain claim to naturalness when considering asymptotic limit distributions for sums, maxima and empirical processes. We discuss implications for aggregation of risk and offer some examples.