Superquantile/CVaR risk measures: second-order theory

R. Tyrrell Rockafellar () and Johannes O. Royset ()
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R. Tyrrell Rockafellar: University of Washington
Johannes O. Royset: Naval Postgraduate School

Annals of Operations Research, 2018, vol. 262, issue 1, No 2, 3-28

Abstract: Abstract Superquantiles, which refer to conditional value-at-risk in the same way that quantiles refer to value-at-risk, 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.

Keywords: Superquantiles; Conditional value-at-risk; Second-order superquantiles; Mixed superquantiles; Spectral measures of risk; Risk envelopes; Risk identifiers; Duality of risk measures; Superquantile regression (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10479-016-2129-0

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