Marshall–Olkin type copulas generated by a global shock

Fabrizio Durante (1) , Stéphane Girard (2) , Gildas Mazo (3)

1 Free University of Bozen-Bolzano
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
3 UCL - Université Catholique de Louvain = Catholic University of Louvain

A way to transform a given copula by means of a univariate function is presented. The resulting copula can be interpreted as the result of a global shock affecting all the components of a system modeled by the original copula. The properties of this copula transformation from the perspective of semi–group action are presented, together with some investigations on the impact on the tail behavior. Finally, the whole methodology is applied to model risk assessment.

Mots clés: Shock models; Marshall–Olkin distributions; Copula

Domaines: Statistiques [math.ST]

Fabrizio Durante, Stéphane Girard, Gildas Mazo. Marshall–Olkin type copulas generated by a global shock. Journal of Applied and Computational Mathematics, 2016, 296, pp.638--648. ⟨hal-01138228v1⟩