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Properties of Distortion Risk Measures

Author

Listed:
  • Alejandro Balbás

    (Universidad Carlos III de Madrid)

  • José Garrido

    (Concordia University)

  • Silvia Mayoral

    (Universidad de Navarra)

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 (VaR α ) or Conditional VaR α (CVaR α ). 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.

Suggested Citation

  • Alejandro Balbás & José Garrido & Silvia Mayoral, 2009. "Properties of Distortion Risk Measures," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 385-399, September.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:3:d:10.1007_s11009-008-9089-z
    DOI: 10.1007/s11009-008-9089-z
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    References listed on IDEAS

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