Tail risk measures, disutility, and extremes: asymptotics and applications

Accurate assessment of extreme risks requires measures that reflect not only the statistical properties of tail events but also decision makers' perceptions of extreme losses. This paper develops disutility-based joint expected shortfall (DJES) and disutility-based truncated expected shortfall (DTES), which incorporate disutility functions to reflect regulators' risk aversion to both the extreme risk and its shortfall. We derive, relying on extreme value techniques, asymptotic approximations of the proposed tail risk measures and construct nonparametric estimators, establishing their consistency under fairly general conditions. This enables reliable extrapolation at ultra-high confidence levels beyond the range of available observations, which we validate through comprehensive finite-sample simulations. In an application to global systemically important insurers (G-SIIs), the proposed measures produce more granular rankings of insurers' systemic vulnerabilities conditional on banking-sector distress than the popular marginal expected shortfall. The results also document time-varying tail risk co-movements between the banking and insurance sectors.