Abstract
We study the asymptotic behavior of the difference between the values at risk (VaR) [Formula: see text] and [Formula: see text] for heavy-tailed random variables [Formula: see text] and [Formula: see text] with [Formula: see text] for application in sensitivity analysis of quantitative operational risk management within the framework of the advanced measurement approach of Basel II (and III). Here, [Formula: see text] describes the loss amount of the present risk profile and [Formula: see text] 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 [Formula: see text] and [Formula: see text]. In particular, if the tail of [Formula: see text] is sufficiently thinner than that of [Formula: see text], then the difference between prior and posterior risk amounts [Formula: see text] is asymptotically equivalent to the expectation (expected loss) of [Formula: see text].
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