Marshall–Olkin type copulas generated by a global shock

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 about the related tail behavior. Finally, the whole methodology is applied to model risk assessment.