In the sixties Mandelbrot already showed that extreme price swings are more likely than some of us think or incorporate in our models. A modern toolbox for analyzing such rare events can be found in the field of extreme value theory. At the core of extreme value theory lies the modelling of...

Tail dependence models for distributions attracted to a max-stable law are fitted using observations above a high threshold. To cope with spatial, high-dimensional data, a rank based M-estimator is proposed relying on bivariate margins only. A data-driven weight matrix is used to minimize the...

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...

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.