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: Numerical evaluation of renewal equations: applications to risk theory and financial models
Abstract: The so-called Renewal Theory is a frequently used methodology in applied mathematics. Renewal Theory is mainly focussed 
	on solving a Volterra integral equation of the second kind known as Renewal Integral EquationAn interesting problem arises 
	when choosing the appropriate numerical tool in order to approximate the solution of the former integral. The decision will 
	be based on the degree of knowledge of function F(x) and some properties of <I>(u). Three methods based in classical 
	methodologies (simulation, product integration and inverting Laplace transform) will be presented and applied to the 
	calculation of ultimate ruin probabilities in the classical case of Risk Theory. The first one is an original simulation 
	scheme, based on the importance sampling technique, that leads to tight interval estimations of the solution of the Renewal 
	equation. In the second one, the use of the so-called Product Integration technique will be considered and compared with 
	other techniques based on the Newton-Cotes methodology. The last method considered is the Gaver-Stehfest algorithm of 
	inverting Laplace transformo This last one, under certain conditions, could be considered as a very fast and accurate 
	method.
Keywords: Modelos matemáticos; Riesgo; Ecuaciones integrales.
Length: 15 pages 
Creation-Date: 1997
Number: 97-18 
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doctra97-18.txt
File-URL: https://eprints.ucm.es/id/eprint/27017/1/9718.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doctra:97-18