Risk Measures with Comonotonic Subadditivity or Convexity and Respecting Stochastic Orders

Taking subadditivity as a main axiom Artzner et.al.(1997, 1999) introduced the coherent risk measures. Song and Yan (2006) introduced risk measures which are comonotonically subadditive or convex. Recently we introduced risk measures which are not only comonotonically subadditive or convex, but also respect the (first) stochastic dominance or stop-loss order, and gived their representations in terms of Choquet integrals w.r.t. distorted probabilities. This talk is based on a joint work with Yongsheng Song