AbstractsMathematics

Extreme-value theory is the branch of statistics concerned with modelling the joint tail of a multivariate distribution. Extreme events are encountered in a large variety of fields, such as hydrology, meteorology, finance, and insurance, and many parametric tail dependence models exist, suitable for modelling high-dimensional extreme events. The main contribution of this thesis consists of two semi-parametric minimum-distance estimation methods, which turn out to be fair competitors to existing likelihood-based methods, allowing for fast and easy estimation of possibly non-differentiable tail dependence models. We also propose a goodness-of-fit test and optimal weighting methods, minimizing the asymptotic variance of the estimators. These estimation methods are used to disentangle sources of tail dependence in European stock markets and to characterize the spatial dependence between extreme windspeeds in the Netherlands. Another contribution of this thesis is related to the statistical modelling of multivariate generalized Pareto distributions. Using a recently developed construction tool, we propose new parametric tail dependence models and illustrate one of them by estimating the probability of a future landslide in northern Sweden. Finally, a new model for dependent defaults in credit risk is proposed, based on a maximum shock mechanism, providing an alternative to the classical model based on sums of Gaussian factors. (SC - Sciences)  – UCL, 2016 Advisors/Committee Members: UCL - SSH/IMAQ/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles, UCL - Faculté des Sciences, Segers, Johan, Denuit, Michel, Lambert, Philippe, Verdonck, Tim, Devolder, Pierre, Rootzen, Holger, Einmahl, John.