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

• Published in: Annals of actuarial science Vol. 9; no. 1; pp. 36 - 57
• Main Authors: Gismondi, Fulvio, Janssen, Jacques, Manca, Raimondo
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.03.2015
• Subjects: Actuarial science; Age; Automobile insurance; Disability; Normal distribution; Random variables; Renewals; Studies; Traffic accidents & safety; Italy; Motorcar insurance; Convolution; Renewal processes; Numerical solution; Non-homogeneous time
• ISSN: 1748-4995; 1748-5002
• DOI: 10.1017/S1748499514000220

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.