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...

Classical extreme-value theory for stationary sequences of random variables can up to a large extent be paraphrased as the study of exceedances over a high threshold. A special role within the description of the temporal dependence between such exceedances is played by the extremal index. Parts...

A complete and user-friendly directory of tails of Archimedean copulas is presented which can be used in the selection and construction of appropriate models with desired properties. The results are synthesized in the form of a decision tree: Given the values of some readily computable...

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.

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.

Tail dependence copulas provide a natural perspective from which one can study the dependence in the tail of a multivariate distribution.For Archimedean copulas with continuously differentiable generators, regular variation of the generator near the origin is known to be closely connected to...

A multivariate extension of the bivariate class of Archimax copulas was recently proposed by Mesiar and Jágr (2013), who asked under which conditions it holds. This paper answers their question and provides a stochastic representation of multivariate Archimax copulas. A few basic properties of...

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...