A folding methodology for multivariate extremes: estimation of the spectral probability measure and actuarial applications

Armelle Guillou (1) , Philippe Naveau (2, 3) , Alexandre You (4)

1 IRMA - Institut de Recherche Mathématique Avancée
2 LSCE - Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]
3 ESTIMR - Extrèmes : Statistiques, Impacts et Régionalisation
4 Societe Generale

In this paper, the folding methodology developed in the context of univariate Extreme Value Theory (EVT) by You et al. is extended to a multivariate framework. Under the usual EVT assumption of regularly varying tails, our multivariate folding allows for the estimation of the spectral probability measure. A new weakly consistent estimator based on the classical empirical estimator is proposed. Its behaviour is illustrated through simulations and an actuarial application relative to reinsurance pricing in the case of an insurance data-set.

Domaines: Statistiques [math.ST]

Armelle Guillou, Philippe Naveau, Alexandre You. A folding methodology for multivariate extremes: estimation of the spectral probability measure and actuarial applications. Scandinavian Actuarial Journal, 2015, 2015 (7), ⟨10.1080/03461238.2013.864326⟩. ⟨hal-01312987⟩