Before revision: We study an asymptotic behaviour of the difference between value-at-risks VaR(L) and VaR(L+S) for heavy-tailed random variables L and S as an application to  sensitivity analysis of quantitative operational risk management in the framework of an advanced measurement approach (AMA) of Basel II.
After revision: We study the asymptotic behaviour of the difference between value-at-risks VaR(L) and VaR(L+S) for heavy-tailed random variables L and S as an application to sensitivity analysis of quantitative operational risk management in the framework of an advanced measurement approach (AMA) of Basel II.