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An Appropriate Way to Switch from the Individual Risk Model to the Collective One

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  • Kuon, S.
  • Radtke, M.
  • Reich, A.

Abstract

For some time now, the convenient and fast calculability of collective risk models using the Panjer-algorithm has been a well-known fact, and indeed practitioners almost always make use of collective risk models in their daily numerical computations. In doing so, a standard link has been preferred for relating such calculations to the underlying heterogeneous risk portfolio and to the approximation of the aggregate claims distribution function in the individual risk model. In this procedure until now, the approximation quality of the collective risk model upon which such calculations are based is unknown. It is proved that the approximation error which arises does not converge to zero if the risk portfolio in question continues to grow. Therefore, necessary and sufficient conditions are derived in order to obtain well-adjusted collective risk models which supply convergent approximations. Moreover, it is shown how in practical situations the previous natural link between the individual and the collective risk model can easily be modified to improve its calculation accuracy. A numerical example elucidates this.

Suggested Citation

  • Kuon, S. & Radtke, M. & Reich, A., 1993. "An Appropriate Way to Switch from the Individual Risk Model to the Collective One," ASTIN Bulletin, Cambridge University Press, vol. 23(1), pages 23-54, May.
  • Handle: RePEc:cup:astinb:v:23:y:1993:i:01:p:23-54_00
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    Cited by:

    1. Roos, Bero, 2007. "On variational bounds in the compound Poisson approximation of the individual risk model," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 403-414, May.
    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.
    3. den Iseger, P. W. & Smith, M. A. J. & Dekker, R., 1997. "Computing compound distributions faster!," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 23-34, June.

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