Superquantile/CVaR Risk Measures: Second-Order Theory

Abstract

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 superquantile/CVaR measures of risk, which represent further "smoothing" by averaging the classical quantities. We also step further and examine the more general "mixed" superquantile/CVaR 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.

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Document Details

Document Type
Technical Report
Publication Date
Jul 17, 2014
Accession Number
ADA615948

Entities

People

  • Johannes Ø. Røyset
  • R. T. Rockafellar

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Applied Mathematics
  • Continuity
  • Distribution Functions
  • Inequalities
  • Integrals
  • Linear Programming
  • Mathematics
  • Operations Research
  • Optimization
  • Probability
  • Random Variables
  • Standards
  • Theorems
  • Topology
  • Two Dimensional

Fields of Study

  • Mathematics

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