Asymptotics of sums of lognormal random variables with Gaussian copula

Let (Y1,…,Yn)(Y1,…,Yn) have a joint nn-dimensional Gaussian distribution with a general mean vector and a general covariance matrix, and let Xi=eYi, Sn=X1+⋯+XnSn=X1+⋯+Xn. The asymptotics of P(Sn>x)P(Sn>x) as n→∞n→∞ are shown to be the same as for the independent case with the same lognormal marginals. In particular, for identical marginals it holds that P(Sn>x)∼nP(X1>x)P(Sn>x)∼nP(X1>x) no matter what the correlation structure is.