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

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 con...

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Bibliographic Details
Published in:Annals of actuarial science 2015-03, Vol.9 (1), p.36-57
Main Authors: Gismondi, Fulvio, Janssen, Jacques, Manca, Raimondo
Format: Article
Language:English
Subjects:
Actuarial science
Age
Automobile insurance
Disability
Normal distribution
Random variables
Renewals
Studies
Traffic accidents & safety
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Summary: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.
ISSN:1748-4995
1748-5002
DOI:10.1017/S1748499514000220