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Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness

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  • Embrechts, Paul
  • Neslehová, Johanna
  • Wüthrich, Mario V.

Abstract

Mainly due to new capital adequacy standards for banking and insurance, an increased interest exists in the aggregation properties of risk measures like Value-at-Risk (VaR). We show how VaR can change from sub to superadditivity depending on the properties of the underlying model. Mainly, the switch from a finite to an infinite mean model gives a completely different asymptotic behaviour. Our main result proves a conjecture made in Barbe et al. [Barbe, P., Fougères, A.L., Genest, C., 2006. On the tail behavior of sums of dependent risks. ASTIN Bull. 36(2), 361-374].

Suggested Citation

  • Embrechts, Paul & Neslehová, Johanna & Wüthrich, Mario V., 2009. "Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 164-169, April.
    • Handle: RePEc:eee:insuma:v:44:y:2009:i:2:p:164-169
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    References listed on IDEAS

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    1. Degen, Matthias & Embrechts, Paul & Lambrigger, Dominik D., 2007. "The Quantitative Modeling of Operational Risk: Between G-and-H and EVT," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 265-291, November.
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    5. Barbe, Philippe & Fougères, Anne-Laure & Genest, Christian, 2006. "On the Tail Behavior of Sums of Dependent Risks," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 361-373, November.
    6. Casper G. de Vries & Gennady Samorodnitsky & Bjørn N. Jorgensen & Sarma Mandira & Jon Danielsson, 2005. "Subadditivity Re–Examined: the Case for Value-at-Risk," FMG Discussion Papers dp549, Financial Markets Group.
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