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Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness
Authors:Paul Embrechts
Institution:ETH Zurich, Department of Mathematics, 8092 Zurich, Switzerland
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].
Keywords:Value-at-Risk  Subadditivity  Dependence structure  Archimedean copula  Aggregation
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