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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

4 Issues per year

Cite Score 2017: 0.96

SCImago Journal Rank (SJR) 2017: 0.455
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Volume 29, Issue 1


Ordering of multivariate risk models with respect to extreme portfolio losses

Georg Mainik / Ludger Rüschendorf
Published Online: 2012-03-12 | DOI: https://doi.org/10.1524/strm.2012.1103


The notion of asymptotic portfolio loss order is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of spectral measures. This allows for analytical and numerical verification in applications. Worst and best case dependence structures with respect to the asymptotic portfolio loss order are determined. Comparison criteria in terms of further stochastic ordering notions are derived. The examples include elliptical distributions and multivariate regularly varying models with Gumbel, Archimedean, and Galambos copulas. Particular interest is paid to the inverse influence of dependence on the diversification of risks with infinite expectations.

Keywords: stochastic ordering; portfolio loss; multivariate regular variation,; spectral measure; extreme risk index

About the article

* Correspondence address: RiskLab, Department of Mathematics, ETH Zurich, Raemistrasse 101, 8092 Zurich, Schweiz,

Published Online: 2012-03-12

Published in Print: 2012-03-01

Citation Information: Statistics & Risk Modeling with Applications in Finance and Insurance, Volume 29, Issue 1, Pages 73–106, ISSN (Print) 2193-1402, DOI: https://doi.org/10.1524/strm.2012.1103.

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