Distortion Risk Measure

As an important risk measure, distortion risk measure plays a more and more important character in modern finance. In recent years, people make many researches on distortion risk measure. This paper mainly summarizes the recent research of distortion risk measure from several points hereinafter.1. The definition and the properties of distortion risk measure. Coherent risk measure, complete distortion risk measure, exhaustive distortion risk measure, adapted distortion risk measure. As well as some common risk measures, and how these common risk measures are expressed as distortion risk measures by using different distortion functions.2. The Relationship between distortion risk measure and stochastic order.3. Distortion risk measures for sums of random variables.4. An application of distortion risk measure.