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The Aggregate Claims Distribution in the Individual Model with Arbitrary Positive Claims

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  • De Pril, Nelson

Abstract

In an earlier paper the author derived a recursion formula which permits the exact computation of the aggregate claims distribution in the individual life model. To save computing time he also proposed an approximative procedure based on the exact recursion. In the present contribution the exact recursion formula and the related approximations are generalized to the individual risk theory model with arbitrary positive claims. Error bounds for the approximations are given and it is shown that they are smaller than those of the Kornya-type approximations.

Suggested Citation

  • De Pril, Nelson, 1989. "The Aggregate Claims Distribution in the Individual Model with Arbitrary Positive Claims," ASTIN Bulletin, Cambridge University Press, vol. 19(1), pages 9-24, April.
    • Handle: RePEc:cup:astinb:v:19:y:1989:i:01:p:9-24_00
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    Citations

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    Cited by:

    1. Sundt, Bjorn, 2002. "Recursive evaluation of aggregate claims distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 297-322, June.
    2. Michel Denuit & Raluca Vernic, 2018. "Bivariate Bernoulli Weighted Sums and Distribution of Single-Period Tontine Benefits," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1403-1416, December.
    3. Ribas, Carme & Marin-Solano, Jesus & Alegre, Antonio, 2003. "On the computation of the aggregate claims distribution in the individual life model with bivariate dependencies," Insurance: Mathematics and Economics, Elsevier, vol. 32(2), pages 201-215, April.
    4. Hurlimann, Werner, 2002. "On the accumulated aggregate surplus of a life portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 27-35, February.
    5. Devolder, Pierre, 2019. "Une alternative a la pension a points : le compte individuel pension en euros," LIDAM Discussion Papers ISBA 2019011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Sundt, Bjorn, 2000. "On error bounds for approximations to multivariate distributions," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 137-144, August.
    7. Denuit, M. & Genest, C. & Marceau, E., 1999. "Stochastic bounds on sums of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 85-104, September.
    8. Denuit, Michel, 2019. "Size-biased transform and conditional mean risk sharing, with application to P2P insurance and tontines," LIDAM Discussion Papers ISBA 2019010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Sundt, Bjorn, 2000. "The multivariate De Pril transform," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 123-136, August.
    10. Dhaene, Jan & Vandebroek, Martina, 1995. "Recursions for the individual model," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 31-38, April.
    11. Cossette, Helene & Gaillardetz, Patrice & Marceau, Etienne & Rioux, Jacques, 2002. "On two dependent individual risk models," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 153-166, April.
    12. Hurlimann, W., 1999. "Non-optimality of a linear combination of proportional and non-proportional reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 219-227, May.
    13. Ambagaspitiya, R. S., 1995. "A family of discrete distributions," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 107-127, May.

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