Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders |
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| Affiliation: | 1. University of Zurich, Department of Banking and Finance, Plattenstrasse 14, 8032 Zurich, Switzerland;2. University of Zurich, Department of Banking and Finance, Plattenstrasse 32, 8032 Zurich, Switzerland;3. ETH Zurich, Department of Mathematics, Rämistrasse 101, 8092 Zurich, Switzerland;1. Zhejiang Provincial Key Laboratory of Advanced Chemical Engineering Manufacture Technology, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China;2. State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, 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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