Additivity Properties for Value-at-Risk under Archimedean Dependence and Heavy-tailedness
by Paul Embrechts of ETH Zurich,
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. .
Keywords: Value-at-Risk, Subadditivity, Dependence structure, Archimedean copula, Aggregation.
Published in: Insurance: Mathematics and Economics, Vol. 44, No. 2, (April 2009), pp. 164-169.