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.  We have different types of results according to the magnitude relationship of thickness of tails of L and S. Especially if the tail of S is enough thinner than the one of L, then  VaR(L+S) - VaR(L) is asymptotically equivalent to an expected loss of S when L and S are independent . We also give some generalized results without the assumption of independence .
We study the asymptotic behaviour of the difference between the Value at Risks VaR(L) and VaR(L+S) for heavy tailed random variables L and S as an application to the sensitivity analysis of quantitative operational risk management in the framework of an advanced measurement approach (AMA) of Basel II. Here the variable L describes the loss amount of the present risk profile and S means the loss amount caused by an additional loss factor. We have different types of results according to the magnitude of the relationship of the thicknesses of the tails of L and S. Especially if the tail of S is sufficiently thinner than that of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the component VaR of S (which is equal to the expected loss of S when L and S are independent ) .
R
an
the
R
value-at-risks
the Value at Risks
R
heavy-tailed
heavy tailed
A
the
A
Here the variable L describes the loss amount of the present risk profile and S means the loss amount caused by an additional loss factor.
R
relationship of thickness of
of the relationship of the thicknesses of the
R
enough thinner than the one
sufficiently thinner than that
A
the difference between prior and posterior risk amounts
R
an
the component VaR of S (which is equal to the
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. We also give some generalized results without the assumption of independence
)