Properties of Distortion Risk Measures

Article

DOI: 10.1007/s11009-008-9089-z

Cite this article as:
Balbás, A., Garrido, J. & Mayoral, S. Methodol Comput Appl Probab (2009) 11: 385. doi:10.1007/s11009-008-9089-z

Abstract

The current literature does not reach a consensus on which risk measures should be used in practice. Our objective is to give at least a partial solution to this problem. We study properties that a risk measure must satisfy to avoid inadequate portfolio selections. The properties that we propose for risk measures can help avoid the problems observed with popular measures, like Value at Risk (VaRα) or Conditional VaRα (CVaRα). This leads to the definition of two new families: complete and adapted risk measures. Our focus is on risk measures generated by distortion functions. Two new properties are put forward for these: completeness, ensuring that the distortion risk measure uses all the information of the loss distribution, and adaptability, forcing the measure to use this information adequately.

Keywords

Risk measures Distortion functions VaRα CVaRα Coherent measures Complete measures Adapted measures 

AMS 2000 Subject Classification

62P05 91B28 

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Alejandro Balbás
    • 1
  • José Garrido
    • 2
  • Silvia Mayoral
    • 3
  1. 1.Universidad Carlos III de MadridMadridSpain
  2. 2.Concordia UniversityMontrealCanada
  3. 3.Universidad de NavarraPamplonaSpain

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