Approximations of value-at-risk as an extreme quantile of a random sum of heavy-tailed random variables

This paper studies the approximation of extreme quantiles of random sums of heavytailed random variables, or, more specifically, subexponential random variables.Akey application of this approximation is the calculation of operational value-at-risk (VaR) for financial institutions in order to determine operational risk capital requirements. This paper follows work by Böcker, Klüppelberg and Sprittulla and makes several advances. These include two new approximations ofVaR and an extension to multiple loss types where the VaR relates to a sum of random sums, each of which is defined by different distributions. The proposed approximations are assessed via a simulation study.