Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders |
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Authors: | Yongsheng Song |
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Affiliation: | Center for Financial Engineering and Risk Management, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China |
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Abstract: | This paper proposes some new classes of risk measures, which are not only comonotonic subadditive or convex, but also respect the (first) stochastic dominance or stop-loss order. We give their representations in terms of Choquet integrals w.r.t. distorted probabilities, and show that if the physical probability is atomless then a comonotonic subadditive (resp. convex) risk measure respecting stop-loss order is in fact a law-invariant coherent (resp. convex) risk measure. |
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Keywords: | G22 |
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