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

Miguel Arturo Usábel Rodrigo
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Miguel Arturo Usábel Rodrigo: Facultad de Ciencias Económicas y Empresariales. Universidad Complutense de Madrid.

No 98-02, Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales from Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales

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.

Keywords: Ultimate non-ruin probability; Laplace transforms; Bromwich-Mellin inversion formula; Gerenalized r-convolution functions. (search for similar items in EconPapers)
Pages: 8 pages
Date: 1998
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