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Between Individual and Collective Model for the Total Claims

Author

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  • Kaas, R.
  • van Heerwaarden, A. E.
  • Goovaerts, M. J.

Abstract

This article studies random variables whose stop-loss rank falls between a certain risk (assumed to be integer-valued and non-negative, but not necessarily of life-insurance type) and the compound Poisson approximation to this risk. They consist of a compound Poisson part to which some independent Bernoulli-type variables are added. Replacing each term in an individual model with such a random variable leads to an approximating model for the total claims on a portfolio of contracts that is computationally almost as attractive as the compound Poisson approximation used in the standard collective model. The resulting stop-loss premiums are much closer to the real values.

Suggested Citation

  • Kaas, R. & van Heerwaarden, A. E. & Goovaerts, M. J., 1988. "Between Individual and Collective Model for the Total Claims," ASTIN Bulletin, Cambridge University Press, vol. 18(2), pages 169-174, November.
    • Handle: RePEc:cup:astinb:v:18:y:1988:i:02:p:169-174_00
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    Cited by:

    1. Simon Mak & Derek Bingham & Yi Lu, 2016. "A regional compound Poisson process for hurricane and tropical storm damage," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(5), pages 677-703, November.
    2. Yang, Jingping & Zhou, Shulin & Zhang, Zhenyong, 2005. "The compound Poisson random variable's approximation to the individual risk model," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 57-77, February.

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