Properties of Distortion Risk Measures
 Alejandro Balbás,
 José Garrido,
 Silvia Mayoral
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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.
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 Title
 Properties of Distortion Risk Measures
 Journal

Methodology and Computing in Applied Probability
Volume 11, Issue 3 , pp 385399
 Cover Date
 20090901
 DOI
 10.1007/s110090089089z
 Print ISSN
 13875841
 Online ISSN
 15737713
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Risk measures
 Distortion functions
 VaR α
 CVaR α
 Coherent measures
 Complete measures
 Adapted measures
 62P05
 91B28
 Industry Sectors
 Authors

 Alejandro Balbás ^{(1)}
 José Garrido ^{(2)}
 Silvia Mayoral ^{(3)}
 Author Affiliations

 1. Universidad Carlos III de Madrid, Madrid, Spain
 2. Concordia University, Montreal, Canada
 3. Universidad de Navarra, Pamplona, Spain