On A Relationship Between Distorted And Spectral Risk Measures

The authors study the relationship between two widely used risk measures, the spectral measures and the distortion risk measures. In both cases, the risk measure can be thought of as a re-weighting of some initial distribution. They prove that spectral risk measures are equivalent to distorted risk pricing measures, or equivalently, spectral risk functions are related to distortion functions. Besides that they prove that distorted measures are absolutely continuous with respect to the original measure.