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Collective Risk Models With Dependence Uncertainty

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  • Liu, Haiyan
  • Wang, Ruodu

Abstract

We bring the recently developed framework of dependence uncertainty into collective risk models, one of the most classic models in actuarial science. We study the worst-case values of the Value-at-Risk (VaR) and the Expected Shortfall (ES) of the aggregate loss in collective risk models, under two settings of dependence uncertainty: (i) the counting random variable (claim frequency) and the individual losses (claim sizes) are independent, and the dependence of the individual losses is unknown; (ii) the dependence of the counting random variable and the individual losses is unknown. Analytical results for the worst-case values of ES are obtained. For the loss from a large portfolio of insurance policies, an asymptotic equivalence of VaR and ES is established. Our results can be used to provide approximations for VaR and ES in collective risk models with unknown dependence. Approximation errors are obtained in both cases.

Suggested Citation

  • Liu, Haiyan & Wang, Ruodu, 2017. "Collective Risk Models With Dependence Uncertainty," ASTIN Bulletin, Cambridge University Press, vol. 47(2), pages 361-389, May.
    • Handle: RePEc:cup:astinb:v:47:y:2017:i:02:p:361-389_00
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    Cited by:

    1. Cossette, Hélène & Marceau, Etienne & Mtalai, Itre, 2019. "Collective risk models with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 153-168.
    2. Oh, Rosy & Jeong, Himchan & Ahn, Jae Youn & Valdez, Emiliano A., 2021. "A multi-year microlevel collective risk model," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 309-328.

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