%0 Report
%A Usábel Rodrigo, Miguel Arturo
%T Calculating ultimate non-ruin probabilities when claim sizes follow a generalized r-convolution distribution function
%J Documentos de Trabajo de la Facultad de Ciencias Económicas y Empresariales
%D 1998
%@ 2255-5471
%U https://hdl.handle.net/20.500.14352/64132
%X 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.
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