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Characterization of upper comonotonicity via tail convex order

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  • Nam, Hee Seok
  • Tang, Qihe
  • Yang, Fan

Abstract

In this paper, we show a characterization of upper comonotonicity via tail convex order. For any given marginal distributions, a maximal random vector with respect to tail convex order is proved to be upper comonotonic under suitable conditions. As an application, we consider the computation of the Haezendonck risk measure of the sum of upper comonotonic random variables with exponential marginal distributions.

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  • Nam, Hee Seok & Tang, Qihe & Yang, Fan, 2011. "Characterization of upper comonotonicity via tail convex order," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 368-373, May.
  • Handle: RePEc:eee:insuma:v:48:y:2011:i:3:p:368-373
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    References listed on IDEAS

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    6. Haezendonck, J. & Goovaerts, M., 1982. "A new premium calculation principle based on Orlicz norms," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 41-53, January.
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    Citations

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    Cited by:

    1. Mao, Tiantian & Hu, Taizhong, 2012. "Second-order properties of the Haezendonck–Goovaerts risk measure for extreme risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 333-343.
    2. Lee, Woojoo & Ahn, Jae Youn, 2014. "On the multidimensional extension of countermonotonicity and its applications," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 68-79.
    3. Cheung, Ka Chun & Lo, Ambrose, 2013. "Characterizations of counter-monotonicity and upper comonotonicity by (tail) convex order," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 334-342.
    4. Ahn, Jae Youn & Shyamalkumar, Nariankadu D., 2014. "Asymptotic theory for the empirical Haezendonck–Goovaerts risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 78-90.
    5. 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.
    6. Tang, Qihe & Yang, Fan, 2014. "Extreme value analysis of the Haezendonck–Goovaerts risk measure with a general Young function," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 311-320.
    7. Changki Kim & Yangho Choi & Woojoo Lee & Jae Youn Ahn, 2013. "Analyzing Herd Behavior in Global Stock Markets: An Intercontinental Comparison," Papers 1308.3966, arXiv.org.
    8. Tang, Qihe & Yang, Fan, 2012. "On the Haezendonck–Goovaerts risk measure for extreme risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 217-227.
    9. 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.
    10. Bellini, Fabio & Rosazza Gianin, Emanuela, 2012. "Haezendonck–Goovaerts risk measures and Orlicz quantiles," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 107-114.

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