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Error Bounds for Compound Poisson Approximations of the Individual Risk Model

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  • De Pril, Nelson
  • Dhaene, Jan

Abstract

The approximation of the individual risk model by a compound Poisson model plays an important role in computational risk theory. It is thus desirable to have sharp lower and upper bounds for the error resulting from this approximation if the aggregate claims distribution, related probabilities or stop-loss premiums are calculated. The aim of this paper is to unify the ideas and to extend to a more general setting the work done in this connection by Bühlmann et al. (1977), Gerber (1984) and others. The quality of the presented bounds is discussed and a comparison with the results of Hipp (1985) and Hipp & Michel (1990) is made.

Suggested Citation

  • De Pril, Nelson & Dhaene, Jan, 1992. "Error Bounds for Compound Poisson Approximations of the Individual Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 22(2), pages 135-148, November.
    • Handle: RePEc:cup:astinb:v:22:y:1992:i:02:p:135-148_00
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    Citations

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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. Denuit, Michel & Lefevre, Claude & Utev, Sergey, 2002. "Measuring the impact of dependence between claims occurrences," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 1-19, February.
    3. 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.
    4. Gerhold, Stefan & Gülüm, I. Cetin, 2019. "Peacocks nearby: Approximating sequences of measures," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2406-2436.
    5. Denuit, Michel & Van Bellegem, Sébastien, 2001. "On the stop-loss and total variation distances between random sums," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 153-165, June.
    6. Claude Lefèvre & Sergey Utev, 1998. "On Order-Preserving Properties of Probability Metrics," Journal of Theoretical Probability, Springer, vol. 11(4), pages 907-920, October.

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