“…Interestingly, in the asymptotically tail-independent case these risk measures may have different rates of convergence or even converge to a constant, e.g., for independent random variables Z 1 , Z 2 we have MES(p) = E(Z 1 ). The asymptotic behavior of MME and MES for a hidden regularly varying random vector Z = (Z 1 , Z 2 ) has been investigated in Das and Fasen-Hartmann [15], furthermore, consistent estimators for these risk measures based on methods from extreme value theory have been proposed; for asymptotic normality of MES see Cai and Musta [8]. On the other hand, the asymptotic behavior of the risk measures as defined in (4) are not particularly well-studied, especially in the context of heavy-tailed asymptotically tail independent risks.…”