Individual risk models need to capture possible correlations as failing to do so typically results in an underestimation of extreme quantiles of the aggregate loss. Such dependence modelling is particularly important for managing credit risk, for instance, where joint defaults are a major cause...

We study the problem of potentially spurious attribution of dependence in moderate to large samples, where both the number of variables and length of variable observations are growing. We approach this question of double asymptotics from both theoretical and empirical perspectives. For...

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.

Let f be a measurable, real function defined in a neighbourhood of infinity. The function f is said to be of generalised regular variation if there exist functions h 6? 0 and g 0 such that f(xt) ? f(t) = h(x)g(t) + o(g(t)) as t ? ? for all x ? (0,?). Zooming in on the remainder term o(g(t))...

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,...