Properties of Distortion Risk Measures Articles uri icon

publication date

  • September 2009

start page

  • 385

end page

  • 399

issue

  • 3

volume

  • 11

international standard serial number (ISSN)

  • 1387-5841

electronic international standard serial number (EISSN)

  • 1573-7713

abstract

  • The current literature does not reach a consensus on which risk measuresshould be used in practice. Our objective is to give at least a partial solution to thisproblem. We study properties that a risk measure must satisfy to avoid inadequateportfolio selections. The properties that we propose for risk measures can help avoid the problems observed with popular measures, like Value at Risk (VaRalfa) or Conditional VaRalfa (CVaRalfa). 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.