Properties of Distortion Risk Measures

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. This research was partially funded by ^1,3 Welzia Management, SGIIC SA, RD Sistemas SA, Comunidad Autónoma de Madrid Grant s-0505/tic/000230, and MEyC Grant BEC2000-1388-C04-03 and by ² the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant 36860-06.