Superquantile/CVaR Risk Measures: Second-Order Theory
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Naval Postgraduate School Monterey United States
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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.
- Statistics and Probability
- Operations Research