Résumé : Multivariate extreme value statistics deals with the estimation of the tail of a multivariate distribution function based on a random sample. Of particular interest is the estimation of the extremal dependence between two or more variables. Accurate modelling of extremal events is needed to better understand the relationship of possibly dependent risks at the tail. We introduce a robust and (asymptotically) unbiased estimator for both the coefficient of tail dependence and probabilities of failure sets. The estimators are obtained by using the minimum density power divergence criterion. The asymptotic properties of both estimators are derived under
some mild regularity conditions. Furthermore, we present an efficient way to compute all the key indicators in a unified approach of the ruin theory and claim reserving methods. The proposed framework allows to derive closed-form formulas for both ruin theory and claim reserves indicators. Finally, we illustrate the practical applicability of the methods on actuarial datasets.
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