Approximation of some multivariate risk measures for Gaussian risks

Gaussian random vectors exhibit the loss of dimension phenomena, which relate to their joint survival tail behaviour. Besides, the fact that the components of such vectors are light-tailed complicates the approximations of various multivariate risk measures significantly. In this contribution we derive precise approximations of marginal mean excess, marginal expected shortfall and multivariate conditional tail expectation of Gaussian random vectors and highlight links with conditional limit theorems. Our study indicates that similar results hold for elliptical and Gaussian like multivariate risks.Comment: To appear in JMV

Gaussian approximation of conditional elliptical copulas

In this paper the limits of elliptical copulas under univariate conditioning are characterized, allowing for the conditioning random variable to have a rapidly varying tail. Further, we investigate the quality of approximation by imposing some weak asymptotic restrictions