Superquantile/CVaR Risk Measures: Second-Order Theory
Article (169.9Kb)Abstract
Superquantiles, which refer to conditional value-at-risk (CVaR) in the same way that
quantiles refer to value-at-risk (VaR), have many advantages in the modeling of risk in finance and engineering. However, some applications may benefit from a further step, from superquantiles to second-
order superquantiles. Measures of risk based on second-order superquantiles have recently been explored
in some settings, but key parts of the theory have been lacking: descriptions of the associated risk envelopes and risk identifiers. Those missing ingredients are supplied in this paper, and moreover not just
for second-order superquantiles, but also for a much broader class of mixed superquantile measures of
risk. Such dualizing expressions facilitate the development of dual methods for mixed and second-order
superquantile risk minimization as well as superquantile regression, a proposed second-order version of
quantile regression.
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