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A Functional Approach to Approximations for the Individual Risk Model

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  • Pitts, Susan M.

Abstract

A functional approach is taken for the total claim amount distribution for the individual risk model. Various commonly used approximations for this distribution are considered, including the compound Poisson approximation, the compound binomial approximation, the compound negative binomial approximation and the normal approximation. These are shown to arise as zeroth order approximations in the functional set-up. By taking the derivative of the functional that maps the individual claim distributions onto the total claim amount distribution, new first order approximation formulae are obtained as refinements to the existing approximations. For particular choices of input, these new approximations are simple to calculate. Numerical examples, including the well-known Gerber portfolio, are considered. Corresponding approximations for stop-loss premiums are given.

Suggested Citation

  • Pitts, Susan M., 2004. "A Functional Approach to Approximations for the Individual Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 34(2), pages 379-397, November.
    • Handle: RePEc:cup:astinb:v:34:y:2004:i:02:p:379-397_01
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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. Pitts, Susan M. & Politis, Konstadinos, 2008. "Approximations for the moments of ruin time in the compound Poisson model," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 668-679, April.

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