Leonardo Rojas Nandayapa

Department of Mathematical Sciences, Aarhus University, Denmark

Tail probabilities of the sum of the components of a Log-elliptical random vector are considered. These random vectors are obtained by an exponential transformation of random vectors with elliptical distributions - a large class of multivariate distributions which includes the multivariate normal, the multivariate-t, normal mixtures and generalized hyperbolics among others. After a brief introduction to this class of distributions, a Monte Carlo estimator for the tail probability of the sum is proposed and analyzed.  In particular, for the multivariate lognormal case it is shown to have optimal theoretical properties.

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