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Tail Comonotonicity and Conservative Risk Measures

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  • Hua, Lei
  • Joe, Harry

Abstract

Tail comonotonicity, or asymptotic full dependence, is proposed as a reasonable conservative dependence structure for modeling dependent risks. Some sufficient conditions have been obtained to justify the conservativity of tail comonotonicity. Simulation studies also suggest that, by using tail comonotonicity, one does not lose too much accuracy but gain reasonable conservative risk measures, especially when considering high scenario risks. A copula model with tail comonotonicity is applied to an auto insurance dataset. Particular models for tail comonotonicity for loss data can be based on the BB2 and BB3 copula families and their multivariate extensions.

Suggested Citation

  • Hua, Lei & Joe, Harry, 2012. "Tail Comonotonicity and Conservative Risk Measures," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 601-629, November.
    • Handle: RePEc:cup:astinb:v:42:y:2012:i:02:p:601-629_00
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    Cited by:

    1. Li, Haijun & Hua, Lei, 2015. "Higher order tail densities of copulas and hidden regular variation," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 143-155.
    2. Das, Bikramjit & Fasen-Hartmann, Vicky, 2018. "Risk contagion under regular variation and asymptotic tail independence," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 194-215.
    3. Das Bikramjit & Fasen-Hartmann Vicky, 2019. "Conditional excess risk measures and multivariate regular variation," Statistics & Risk Modeling, De Gruyter, vol. 36(1-4), pages 1-23, December.
    4. Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
    5. Su, Jianxi & Hua, Lei, 2017. "A general approach to full-range tail dependence copulas," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 49-64.
    6. Gribkova, N.V. & Su, J. & Zitikis, R., 2022. "Inference for the tail conditional allocation: Large sample properties, insurance risk assessment, and compound sums of concomitants," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 199-222.
    7. Bikramjit Das & Vicky Fasen, 2016. "Risk contagion under regular variation and asymptotic tail independence," Papers 1603.09406, arXiv.org, revised Apr 2017.

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