By Greg N. Gregoriou (eds.)
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8 million for BL1 and BL2, respectively. 750 Scale parameter 1677 601 Expected loss 282,429 179,893 Unexpected loss 1,596,046 990,471 1,313,617 810,578 Regulatory capital charge10 observed losses, respectively. The higher value for Business Line 1 is not surprising as BL1 is characterized by a higher proportion of severe losses. This is reﬂected in the aggregate loss distribution with a fatter tail and, consequently, proportionally heavier capital requirements. 3 Sensitivity analysis Next, we move on to the analysis of the impact of the collection threshold on the regulatory capital charge.
Xn ) be the ordered sample of observations. Consider m candidate thresholds U1 , . . , Um such that xn−i , . . , xn > Ui for i = 1, . . , m. 2 For each threshold Ui , use the weighted average of Hill estimators proposed in Huisman et al. (2001) to estimate the tail index ξi of the GPD distribution. This method corrects for the small-sample bias of the original Hill estimator. 3 Then compute the maximum likelihood estimator of the scale parameter βi of the GPD, with the tail index ξi ﬁxed to the value obtained in step 2.
In contrast, the ﬁrm may be willing to alter their holdings of expensive instruments such as Treasury bonds. Thus, our primary objective is minimizing perturbations to the ﬁrm’s original portfolio η, which is assumed to be its preferred allocation. Instead, the ﬁrm is able to specify the cost of rebalancing each individual asset from their perspective when ﬁnding the acceptable portfolio’s solution. 4, one possibility simply has the rebalancing cost for each asset being equal to its price. This special case minimizes the dollar-denominated amount of rebalancing.