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Distortion Riskmetrics On General Spaces

Author

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  • Wang, Qiuqi
  • Wang, Ruodu
  • Wei, Yunran

Abstract

The class of distortion riskmetrics is defined through signed Choquet integrals, and it includes many classic risk measures, deviation measures, and other functionals in the literature of finance and actuarial science. We obtain characterization, finiteness, convexity, and continuity results on general model spaces, extending various results in the existing literature on distortion risk measures and signed Choquet integrals. This paper offers a comprehensive toolkit of theoretical results on distortion riskmetrics which are ready for use in applications.

Suggested Citation

  • Wang, Qiuqi & Wang, Ruodu & Wei, Yunran, 2020. "Distortion Riskmetrics On General Spaces," ASTIN Bulletin, Cambridge University Press, vol. 50(3), pages 827-851, September.
    • Handle: RePEc:cup:astinb:v:50:y:2020:i:3:p:827-851_6
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    Citations

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    Cited by:

    1. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2023. "Risk sharing, measuring variability, and distortion riskmetrics," Papers 2302.04034, arXiv.org.
    2. Qiuqi Wang & Ruodu Wang & Ricardas Zitikis, 2021. "Risk measures induced by efficient insurance contracts," Papers 2109.00314, arXiv.org, revised Sep 2021.
    3. Wang, Qiuqi & Wang, Ruodu & Zitikis, Ričardas, 2022. "Risk measures induced by efficient insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 56-65.
    4. Xia Han & Ruodu Wang & Xun Yu Zhou, 2022. "Choquet regularization for reinforcement learning," Papers 2208.08497, arXiv.org.
    5. Yuyu Chen & Paul Embrechts & Ruodu Wang, 2022. "An unexpected stochastic dominance: Pareto distributions, dependence, and diversification," Papers 2208.08471, arXiv.org, revised Mar 2024.
    6. Fuchs Sebastian & Trutschnig Wolfgang, 2020. "On quantile based co-risk measures and their estimation," Dependence Modeling, De Gruyter, vol. 8(1), pages 396-416, January.
    7. Xiaoqing Liang & Ruodu Wang & Virginia Young, 2021. "Optimal Insurance to Maximize RDEU Under a Distortion-Deviation Premium Principle," Papers 2107.02656, arXiv.org, revised Feb 2022.
    8. Bellini, Fabio & Fadina, Tolulope & Wang, Ruodu & Wei, Yunran, 2022. "Parametric measures of variability induced by risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 270-284.
    9. Barczy, Mátyás & K. Nedényi, Fanni & Sütő, László, 2023. "Probability equivalent level of Value at Risk and higher-order Expected Shortfalls," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 107-128.
    10. Yunran Wei & Ricardas Zitikis, 2022. "Assessing the difference between integrated quantiles and integrated cumulative distribution functions," Papers 2210.16880, arXiv.org, revised Apr 2023.
    11. Silvana Pesenti & Qiuqi Wang & Ruodu Wang, 2020. "Optimizing distortion riskmetrics with distributional uncertainty," Papers 2011.04889, arXiv.org, revised Feb 2022.
    12. Fabio Bellini & Tolulope Fadina & Ruodu Wang & Yunran Wei, 2020. "Parametric measures of variability induced by risk measures," Papers 2012.05219, arXiv.org, revised Apr 2022.
    13. Wei, Yunran & Zitikis, Ričardas, 2023. "Assessing the difference between integrated quantiles and integrated cumulative distribution functions," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 163-172.
    14. Wiesel Johannes & Zhang Erica, 2023. "An optimal transport-based characterization of convex order," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-15, January.
    15. Fuchs Sebastian & Trutschnig Wolfgang, 2020. "On quantile based co-risk measures and their estimation," Dependence Modeling, De Gruyter, vol. 8(1), pages 396-416, January.
    16. Wei Wang & Huifu Xu, 2023. "Preference robust state-dependent distortion risk measure on act space and its application in optimal decision making," Computational Management Science, Springer, vol. 20(1), pages 1-51, December.
    17. Xia Han & Ruodu Wang & Qinyu Wu, 2023. "Monotonic mean-deviation risk measures," Papers 2312.01034, arXiv.org.
    18. Carole Bernard & Silvana M. Pesenti & Steven Vanduffel, 2022. "Robust Distortion Risk Measures," Papers 2205.08850, arXiv.org, revised Mar 2023.
    19. Ruodu Wang & Qinyu Wu, 2022. "Quasi-convexity in mixtures for generalized rank-dependent functions," Papers 2209.03425, arXiv.org.

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