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Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders

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  • Song, Yongsheng
  • Yan, Jia-An

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.

Suggested Citation

  • Song, Yongsheng & Yan, Jia-An, 2009. "Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 459-465, December.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:3:p:459-465
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    References listed on IDEAS

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