Superquantile/CVaR Risk Measures: Second-Order Theory
Loading...
Authors
Royset, Johannes O.
Rockafellar, R. Tyrrell
Subjects
superquantiles
conditional value-at-risk
second-order superquantiles
mixed superquantiles
spectral measures of risk
risk envelopes
risk identifiers
duality of risk measures
superquantile regression
conditional value-at-risk
second-order superquantiles
mixed superquantiles
spectral measures of risk
risk envelopes
risk identifiers
duality of risk measures
superquantile regression
Advisors
Date of Issue
2015-11-05
Date
November 5, 2015
Publisher
Language
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.
Type
Article
Description
Series/Report No
Department
Operations Research (OR)
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
U.S. Air Force Office of Scientific Research grant FA9550-11-1-0206
U.S. Air Force Office of Scientific Research grant F1ATAO1194GOO1
DARPA grant HR0011517798
U.S. Air Force Office of Scientific Research grant F1ATAO1194GOO1
DARPA grant HR0011517798
Funding
U.S. Air Force Office of Scientific Research grant FA9550-11-1-0206
U.S. Air Force Office of Scientific Research grant F1ATAO1194GOO1
DARPA grant HR0011517798
U.S. Air Force Office of Scientific Research grant F1ATAO1194GOO1
DARPA grant HR0011517798
Format
28 p.
Citation
R.T. Rockafellar and J.O. Royset, 2016, "Superquantile/CVaR Risk Measures: Second-Order Theory," Annals of Operations Research, to appear.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.