Convergence of a sequence of bivariate Archimedean copulas to another Archimedean copula or to the comonotone copula is shown to be equivalent with convergence of the corresponding sequence of Kendall distribution functions. No extra differentiability conditions on the generators are needed.

The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk model, where the total claim size in a...

In a stationary sequence of random variables, high-threshold exceedances may cluster together. Two approximations of such a cluster's distribution are established. These justify and generalize sampling schemes for clusters of extremes already known for Markov chains.

One of the features inherent in nested Archimedean copulas, also called hierarchical Archimedean copulas, is their rooted tree structure. A nonparametric, rank-based method to estimate this structure is presented. The idea is to represent the target structure as a set of trivariate structures,...

Conditions are given under which the empirical copula process associated with a random sample from a bivariate continuous distribution has a smaller asymptotic covariance function than the standard empirical process based on observations from the copula. Illustrations are provided and...

The quantification of diversification benefits due to risk aggregation plays a prominent role in the (regulatory) capital management of large firms within the financial industry. However, the complexity of today's risk landscape makes a quantifiable reduction of risk concentration a challenging...

Let X1,X2,... be independent observations from the absolutely continuous distribution function F with quantile function Q. The density of the normalized order statistic Xn-kn+1:n converges locally uniformly to the standard normal density for any sequence kn with kn--[infinity] and kn/n--0 if and...