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On the Exact Calculation of the Aggregate Claims Distribution in the Individual Life Model

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  • Waldmann, Karl-Heinz

Abstract

An iteration scheme is derived for calculating the aggregate claims distribution in the individual life model. The (exact) procedure is an efficient reformulation of De Pril's (1986) algorithm, considerably reducing both the number of arithmetic operations to be carried out and the number of data to be kept at each step of iteration. Scaling functions are used to stabilize the algorithm in case of a portfolio with a large number of policies. Some numerical results are displayed to demonstrate the efficiency of the method.

Suggested Citation

  • Waldmann, Karl-Heinz, 1994. "On the Exact Calculation of the Aggregate Claims Distribution in the Individual Life Model," ASTIN Bulletin, Cambridge University Press, vol. 24(1), pages 89-96, May.
    • Handle: RePEc:cup:astinb:v:24:y:1994:i:01:p:89-96_00
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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. 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.
    4. Dhaene, Jan & Vandebroek, Martina, 1995. "Recursions for the individual model," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 31-38, April.
    5. Alvaro Tomassetti & Angelo Manna & Sabrina Pucci, 1995. "Risk Theory: Exact Calculations In The Individual Risk Model; Some Methods," Working Papers 029, Risk and Insurance Archive.
    6. 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.
    7. 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.

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