First and Second-order Asymptotics for Operational Risk Based on a Spectral Risk Measure

Spectral risk measures (SRMs) was first introduced by Acerbi (2002), which take account of risk aversion of a decision maker. In this paper, we study the asymptotics of SRMs with risk severity distribution from the max-domain of attraction of an extreme value distribution. More precisely, we get the first-order asymptotics of SRMs according to the max-domains of the Frechet, Weibull and Gumbel distributions, respectively. We also investigate the second-order asymptotics for operational risk SRMs under the theory of second-order regular variation and second-order subexponentiality.