Superquantile/CVaR Risk Measures: Second-Order Theory

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.

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Document Details

Document Type
Technical Report
Publication Date
Nov 05, 2015
Accession Number
AD1014612

Entities

People

  • Johannes Ø. Røyset
  • R. T. Rockafellar

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Continuity
  • Distribution Functions
  • Inequalities
  • Integrals
  • Linear Programming
  • Normal Distribution
  • Notation
  • Operations Research
  • Optimization
  • Probability
  • Random Variables
  • Standards
  • Statistics
  • Theorems
  • Topology
  • Two Dimensional

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Aviation Safety Risk Assessment.