Template-type: ReDIF-Paper 1.0
Author-Name: Miguel Arturo Usábel Rodrigo
Author-Workplace-Name:
 Facultad de Ciencias Económicas y Empresariales. Universidad Complutense de Madrid.
Title: Calculating ultimate non-ruin probabilities when claim sizes follow a generalized r-convolution distribution function
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.
Length: 8 pages 
Creation-Date: 1998 
Number: 98-02 
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doctra98-02.txt
File-URL: https://eprints.ucm.es/id/eprint/27083/1/9802.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doctra:98-02