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Distortion Risk Measures : Coherence and Stochastic Dominance

In this paper it is proved that a concave distortion function is a necessary and sufficient condition for coherence, and a strictly concave distortion function is a necessary and sufficient condition for strict consistency with second order stochastic dominance. The results are related to current risk measures used in practice, such as value-at-risk (VaR) and the conditional tail expectation (CTE), also known as tail-VaR and to Wang’s premium principles.