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Calculating ultimate non-ruin probabilities when claim sizes follow a generalized r-convolution distribution function

Author

Listed:
  • Miguel Arturo Usábel Rodrigo

    ( Facultad de Ciencias Económicas y Empresariales. Universidad Complutense de Madrid.)

Abstract

The non-ruin probability, for initial reserves u, in the classical can be calculated using the so-called Bromwich-Mellin inversion formula, an outstanding result from Residues Theory first introduced for these purposes by Seal(1977) for exponential claim size. We will use this technique when claim sizes follow a generalized r-convolution function distribution. Some of the most frequently used heavy-tailed distributions in actuarial science belongs to this family. Thorin(1977) or Berg(1981) proved that Pareto distributions are members of this family; so Thorin(1977) did with Log-normal distributions.

Suggested Citation

  • Miguel Arturo Usábel Rodrigo, 1998. "Calculating ultimate non-ruin probabilities when claim sizes follow a generalized r-convolution distribution function," Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales 98-02, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
    • Handle: RePEc:ucm:doctra:98-02
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