Usábel Rodrigo, Miguel Arturo2023-06-212023-06-2119982255-5471https://hdl.handle.net/20.500.14352/64132The 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.engAtribución-NoComercial-CompartirIgual 3.0 Españahttps://creativecommons.org/licenses/by-nc-sa/3.0/es/Calculating ultimate non-ruin probabilities when claim sizes follow a generalized r-convolution distribution functiontechnical reporthttps://economicasyempresariales.ucm.es/working-papers-cceeopen accessUltimate non-ruin probabilityLaplace transformsBromwich-Mellin inversion formulaGerenalized r-convolution functions.Probabilidades (Matemáticas)