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Coherent Distortion Risk Measures and Higher-Order Stochastic Dominances

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  • Fabio Bellini
  • Camilla Caperdoni

Abstract

We show that the only coherent distortion risk measure that is consistent with respect to 3-convex order and hence with stochastic dominance of order 3 is the expected value, thus generalizing previous results of Hurlimann and solving a problem posed by Yamai and Yoshiba.

Suggested Citation

  • Fabio Bellini & Camilla Caperdoni, 2007. "Coherent Distortion Risk Measures and Higher-Order Stochastic Dominances," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(2), pages 35-42.
    • Handle: RePEc:taf:uaajxx:v:11:y:2007:i:2:p:35-42
    DOI: 10.1080/10920277.2007.10597446
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    Cited by:

    1. Gabriela Zeller & Matthias Scherer, 2023. "Risk mitigation services in cyber insurance: optimal contract design and price structure," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 502-547, April.
    2. Alois Pichler, 2017. "A quantitative comparison of risk measures," Annals of Operations Research, Springer, vol. 254(1), pages 251-275, July.
    3. Alois Pichler, 2024. "Higher order measures of risk and stochastic dominance," Papers 2402.15387, arXiv.org.
    4. Pichler, Alois & Shapiro, Alexander, 2015. "Minimal representation of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 184-193.

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