We study the asymptotic behavior of the difference between the values at risk
VaR(L) and VaR(L+S) for heavy tailed random variables L and S for application
in sensitivity analysis of quantitative operational risk management within the
framework of the advanced measurement approach of Basel II (and III). Here L
describes the loss amount of the present risk profile and S describes the loss
amount caused by an additional loss factor. We obtain different types of
results according to the relative magnitudes of the thicknesses of the tails of
L and S. In particular, if the tail of S is sufficiently thinner than the tail
of L, then the difference between prior and posterior risk amounts VaR(L+S) -
VaR(L) is asymptotically equivalent to the expectation (expected loss) of S.Comment: 21 pages, 1 figure, 4 tables, forthcoming in International Journal of
Theoretical and Applied Finance (IJTAF