The asymptotic behavior of systemic expected shortfall and marginal expected shortfall under extreme losses

Abstract

The paper considers the asymptotics of the systemic expected shortfall (SES) and the marginal expected shortfall (MES) in systemic risks. We mainly consider individual losses to be the products of primary variables and random weights, where a dependence structure exists between the primary variable and the corresponding random weight for each loss. When the distributions of the primary variables belong to the intersection of long-tailed and dominatedly varying-tailed distribution function classes, we obtain the asymptotics of SES and MES of individual losses. Particularly, under the coherent capital allocation, more precise estimations for SES and MES of individual losses are presented for the regularly varying-tailed primary variables. Some numerical studies are conducted to check the accuracy of the obtained results.