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Approximation of Some Multivariate Risk Measures for Gaussian Risks

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  • E. Hashorva

Abstract

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.

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  • E. Hashorva, 2018. "Approximation of Some Multivariate Risk Measures for Gaussian Risks," Papers 1803.06922, arXiv.org, revised Oct 2018.
    • Handle: RePEc:arx:papers:1803.06922
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    1. Balkema, A.A. & Embrechts, P. & Nolde, N., 2010. "Meta densities and the shape of their sample clouds," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1738-1754, August.
    2. Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
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    5. Krzysztof Dȩbicki & Enkelejd Hashorva & Lanpeng Ji & Chengxiu Ling, 2015. "Extremes of order statistics of stationary processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 229-248, June.
    6. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2017. "Multivariate extensions of expectiles risk measures," Post-Print hal-01478930, HAL.
    7. Wolfgang Bischoff & Frank Miller & Enkelejd Hashorva & Jürg Hüsler, 2003. "Asymptotics of a Boundary Crossing Probability of a Brownian Bridge with General Trend," Methodology and Computing in Applied Probability, Springer, vol. 5(3), pages 271-287, September.
    8. Landsman, Zinoviy & Makov, Udi & Shushi, Tomer, 2016. "Multivariate tail conditional expectation for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 216-223.
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    10. Hashorva, Enkelejd & Jaworski, Piotr, 2012. "Gaussian approximation of conditional elliptical copulas," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 397-407.
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