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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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    Citations

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    Cited by:

    1. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Aug 2015.
    2. Grigorova Miryana, 2014. "Stochastic dominance with respect to a capacity and risk measures," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 1-37, December.
    3. repec:eee:ejores:v:262:y:2017:i:2:p:720-732 is not listed on IDEAS
    4. Grigorova Miryana, 2014. "Stochastic orderings with respect to a capacity and an application to a financial optimization problem," Statistics & Risk Modeling, De Gruyter, vol. 31(2), pages 1-31, June.
    5. Miryana Grigorova, 2011. "Stochastic dominance with respect to a capacity and risk measures," Working Papers hal-00639667, HAL.
    6. Cont Rama & Deguest Romain & He Xue Dong, 2013. "Loss-based risk measures," Statistics & Risk Modeling, De Gruyter, vol. 30(2), pages 133-167, June.
    7. Rama Cont & Romain Deguest & Xuedong He, 2011. "Loss-Based Risk Measures," Papers 1110.1436, arXiv.org, revised Apr 2013.
    8. repec:eee:insuma:v:77:y:2017:i:c:p:24-37 is not listed on IDEAS
    9. Rama Cont & Romain Deguest & Xuedong He, 2011. "Loss-Based Risk Measures," Working Papers hal-00629929, HAL.
    10. Goovaerts, Marc & Linders, Daniël & Van Weert, Koen & Tank, Fatih, 2012. "On the interplay between distortion, mean value and Haezendonck–Goovaerts risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 10-18.
    11. Jaume Belles-Sampera & Montserrat Guillén & Miguel Santolino, 2013. "“The use of flexible quantile-based measures in risk assessment”," IREA Working Papers 201323, University of Barcelona, Research Institute of Applied Economics, revised Dec 2013.
    12. Gianni Bosi & Magalì Zuanon, 2012. "A note on the axiomatization of Wang premium principle by means of continuity considerations," Economics Bulletin, AccessEcon, vol. 32(4), pages 3158-3165.
    13. Labopin-Richard T. & Gamboa F. & Garivier A. & Iooss B., 2016. "Bregman superquantiles. Estimation methods and applications," Dependence Modeling, De Gruyter Open, vol. 4(1), pages 1-33, March.
    14. Jaume Belles-Sampera & Montserrat Guillén & Miguel Santolino, 2013. "“Beyond Value-at-Risk: GlueVaR Distortion Risk Measures”," IREA Working Papers 201302, University of Barcelona, Research Institute of Applied Economics, revised Feb 2013.

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