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Additivity properties for value-at-risk under archimedean dependence and heavy-tailedness. (English) Zbl 1163.91431

Summary: 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 P. Barbe et al. [On the tail behavior of sums of dependent risks. ASTIN Bull. 36, No. 2, 361–374 (2006)].

MSC:

91B30 Risk theory, insurance (MSC2010)

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