# Approximation of some multivariate risk measures for Gaussian risks

*Enkelejd Hashorva*

*Journal of Multivariate Analysis*, 2019, vol. 169, issue C, 330-340

**Abstract:**
Gaussian random vectors exhibit the loss of dimension phenomenon, which relates to their joint survival tail behavior. 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.

**Keywords:** Conditional limit theorem; Gaussian random vectors; Marginal expected shortfall; Marginal mean excess; Multivariate conditional tail expectation (search for similar items in EconPapers)

**Date:** 2019

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