Superquantile/CVaR Risk Measures: Second-Order Theory
NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF OPERATIONS RESEARCH
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Superquantile risk, also known as conditional value-at-risk CVaR, is widely used as a coherent measure of risk due to its improved properties over those of quantile risk value-at-risk. In this paper, we consider second-order superquantileCVaR measures of risk, which represent further smoothing by averaging the classical quantities. We also step further and examine the more general mixed superquantileCVaR measures of risk with fundamental importance in dual utility theory. We establish representations of these mixed and second-order superquantile risk measures in terms of risk profiles, risk envelopes, and risk identifiers. The expressions facilitate the development of dual methods for mixed and second-order superquantile risk minimization as well as superquantile regression, a second-order version of quantile regression.
- Statistics and Probability
- Operations Research