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Non-homogeneous time convolutions, renewal processes and age-dependent mean number of motorcar accidents

Published online by Cambridge University Press:  22 August 2014

Fulvio Gismondi ,
Jacques Janssen  and
Raimondo Manca
Fulvio Gismondi
Affiliation:
University Guglielmo Marconi, Via Plinio 44, 00193 Roma, Italy
Jacques Janssen
Affiliation:
Solvay Business School ULB, 4 Rue de la Colline, 1480 Tubize, Belgium
Raimondo Manca*
Affiliation:
University of Rome La Sapienza, via del Castro Laurenziano 9, 00161 Roma, Italy
*
*Correspondence to: Raimondo Manca, University of Rome La Sapienza, via del Castro Laurenziano 9, 00161 Roma, Italy. Tel: +39 064 976 6507. Fax: +39 064 976 6765. E-mail: raimondo.manca@uniroma1.it
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Abstract

Non-homogeneous renewal processes are not yet well established. One of the tools necessary for studying these processes is the non-homogeneous time convolution. Renewal theory has great relevance in general in economics and in particular in actuarial science, however, most actuarial problems are connected with the age of the insured person. The introduction of non-homogeneity in the renewal processes brings actuarial applications closer to the real world. This paper will define the non-homogeneous time convolutions and try to give order to the non-homogeneous renewal processes. The numerical aspects of these processes are then dealt with and a real data application to an aspect of motorcar insurance is proposed.

Keywords

Non-homogeneous timeConvolutionRenewal processesNumerical solutionMotorcar insurance
Type
Papers
Information
Annals of Actuarial Science , Volume 9 , Issue 1 , March 2015 , pp. 36 - 57
Copyright
© Institute and Faculty of Actuaries 2014 

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