Before revision:  We then compute this function explicitly for several families of copulas, such as the Gaussian copula, the copulas of Gaussian mean-variance mixtures and a class of Archimedean copulas. As an illustration, we compute the left tail asymptotics for a portfolio of call options in the multidimensional Black-Scholes model .
After revision:  We then compute this function explicitly for several families of copulas, such as the Gaussian copula, the copulas of Gaussian mean-variance mixtures and a class of Gaussian mixture models, certain Archimedean copulas and extreme value copulas. The new measure allows to quantify the tail behavior of certain functionals of weakly dependent random vectors at the log scale .