Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T16:58:35.307Z Has data issue: false hasContentIssue false
  • English
  • Français

Vehicle and Fleet Random Effects in a Model of Insurance Rating for Fleets of Vehicles

Published online by Cambridge University Press:  17 April 2015

Jean-François Angers ,
Denise Desjardins ,
Georges Dionne  and
François Guertin
Jean-François Angers
Affiliation:
Center for Research on Transportation, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montreal, Canada, H3C 3J7
Denise Desjardins
Affiliation:
Center for Research on Transportation, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montreal, Canada, H3C 3J7
Georges Dionne
Affiliation:
Canada Research Chair in Risk Management, HEC Montréal, 3000, Chemin de la Côte-Sainte-Catherine, Montreal (Qc) Canada, H3T 2A7, Tel.: (514)340-6596, Fax: (514)340-5019, E-mail: georges.dionne@hec.ca
François Guertin
Affiliation:
Center for Research on Transportation, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montreal, Canada, H3C 3J7
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We are proposing a parametric model to rate insurance for vehicles belonging to a fleet. The tables of premiums presented take into account past vehicle accidents, observable characteristics of the vehicles and fleets, and violations of the road-safety code committed by drivers and carriers. The premiums are also adjusted according to accidents accumulated by the fleets over time. The proposed model accounts directly for explicit changes in the various components of the probability of accidents. It represents an extension of bonus malus-type automobile insurance models for individual premiums (Lemaire, 1985; Dionne and Vanasse, 1989 and 1992; Pinquet, 1997 and 1998; Frangos and Vrontos, 2001; Purcaru and Denuit, 2003). The extension adds a fleet effect to the vehicle effect so as to account for the impact that the unobservable characteristics or actions of carriers can have on truck accident rates. This form of rating makes it possible to visualize what impact the behaviors of owners and drivers can have on the predicted rate of accidents and, consequently, on premiums. The results are compared to those of the semiparametric approach.

Keywords

Fleet of vehiclesrandom effectsvehicle effectfleet effectinsurance ratingbehaviors of owners and driversPoisson, gammaDirichletparametric model
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 1 , May 2006 , pp. 25 - 77
Copyright
Copyright © ASTIN Bulletin 2006

Footnotes

1

Département de mathématiques et de statistique, Université de Montréal and CRT.

2

CRT, Université de Montréal

3

HEC Montréal, CRT, CIRPÉE, and THEMA (France)

4

RQCHP and CRT, Université de Montréal

References

Abowd, J.-M., Kramarz, F., and Margolis, D.N. (1999) High Wage Workers and High Wage Firms. Econometrica 67, 251–333.CrossRefGoogle Scholar
Angers, J.F., Desjardins, D., Dionne, G., and Guertin, F. (2006) Individual and Firms Random Effects in the Estimation of Event Distributions. Working Paper, Canada Research Chair in Risk Management, HEC Montréal, and CRT, Université de Montréal.Google Scholar
Angers, J.F., Desjardins, D., and Dionne, G. (2004) Modèle bayésien de tarification de l’assurance des flottes de véhicules. L’Actualité économique 80, 253–305.CrossRefGoogle Scholar
Dionne, G., Desjardins, D., and Pinquet, J. (1999) L’évaluation du risque d’accident des transporteurs en fonction de leur secteur d’activité, de la taille de leur flotte et de leur dossier d’infractions. Research report 2000-28, Centre de recherche sur les transports, Université de Montréal, 154 p.Google Scholar
Dionne, G., Desjardins, D., and Pinquet, J. (2001) Experience Rating Schemes for Fleets of Vehicles. ASTIN Bulletin 31, 85–109.Google Scholar
Dionne, G., Desjardins, D., Ingabire, M.G., and Akdim, R. (2001) La perception du risque d’être arrêté chez les camionneurs et transporteurs routiers. Research report 2001-05, Centre de recherche sur les transports, Université de Montréal, 139 p.Google Scholar
Dionne, G., Laberge-Nadeau, C., Desjardins, D., Messier, S., and Maag, U. (1999) Analysis of the Economic Impact of Medical and Optometric Driving Standards on Costs Incurred by Trucking Firms and on the Social Cost of Traffic Accidents. In Automobile Insurance: Road Safety, New Drivers, Risks, Insurance Fraud and Regulation (ed. Dionne, G. and LabergeNadeau, C.), pp. 323–351, Kluwer Academic Publishers, Boston.CrossRefGoogle Scholar
Dionne, G. and Vanasse, C. (1989) A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component. ASTIN Bulletin 19, 199–212.CrossRefGoogle Scholar
Dionne, G. and Vanasse, C. (1992) Automobile Insurance Ratemarking in the Presence of Asymmetrical Information. Journal of Applied Econometrics 7, 149–165.CrossRefGoogle Scholar
Frangos, N. and Vrontos, S.D. (2001) Design of Optimal Bonus malus Systems with a Frequency and a Severity Component on an Individual Basis in Automobile Insurance. ASTIN Bulletin 31, 1–22.CrossRefGoogle Scholar
Fluet, C. (1999) Commercial Vehicle Insurance: Should Fleet Policies Differ from Single Vehicle Plans? In Automobile Insurance: Road Safety, New Drivers, Risks Insurance Fraud and Regulation (ed. Dionne, G. and Laberge-Nadeau, C.), 101–117, Kluwer Academic Publishers, Boston.CrossRefGoogle Scholar
Gouriéroux, C. (1999) Statistiques de l’assurance. Economica, Paris, 297 p.Google Scholar
Gouriéroux, C., Monfort, A., and Trognon, A. (1984) Pseudo Maximum Likelihood Methods: Application to Poisson Models. Econometrica 52, 701–720.CrossRefGoogle Scholar
Gradshteyn, I.S. and Ryzhik, I.M. (1980) Table of Integrals, Series, and Products. Academic Press Inc., New York, 1160 pages.Google Scholar
Hausman, J.A., Hall, B.H., and Griliches, Z. (1984) Econometric Models for Count Data with an Application to the Patents– R&D Relationship. Econometrica 52, 909–938.CrossRefGoogle Scholar
Johnson, N. and Kotz, K. (1969) Discrete Distributions. Houghton Mifflin, Boston, 328 p.Google Scholar
Lange, K. (1999) Numerical Analysis for Statisticians. Springer: New York, section 21.2, 189–198.Google Scholar
Lemaire, J. (1985) Automobile Insurance: Actuarial Models. Huebner International Series on Risk, Insurance and Economic Security, Kluwer Academic Publishers, Boston, 248 p.CrossRefGoogle Scholar
Lemaire, J. (1995) Bonus Malus Systems in Automobile Insurance. Kluwer Academic Publishers, Boston, 283 p.CrossRefGoogle Scholar
Marie-Jeanne, P. (1994) Problèmes spécifiques des flottes automobiles. Proceedings of the ISUP conference “Cours Avancés sur l’Assurance Automobile.” Google Scholar
Moses, L.N. and Savage, I. (1994) The Effect of Firm Characteristics on Truck Accidents. Accident Analysis & Prevention 26, 173–179.CrossRefGoogle ScholarPubMed
Moses, L.N. and Savage, I. (1996) Identifying Dangerous Trucking Firms. Risk Analysis 16, 359–366.CrossRefGoogle Scholar
Pinquet, J. (1997) Allowance for Cost of Claims in Bonus malus Systems. ASTIN Bulletin 27, 23–40.CrossRefGoogle Scholar
Pinquet, J. (1998) Designing Optimal Bonus malus Systems from Different Types of Claims. ASTIN Bulletin 28, 205–220.CrossRefGoogle Scholar
Pinquet, J. (2000) Experience Rating through Heterogeneous Models. In Handbook of Insurance, (ed. Dionne, G.), Kluwer Academic Publishers, Boston, 459–500.CrossRefGoogle Scholar
Purcaru, O. and Denuit, M. (2003) Dependence in Dynamic Claim Frequency Credibility Models. ASTIN Bulletin 33, 23–40.CrossRefGoogle Scholar
Teugels, J.L. and Sundt, B. (1991) A Stop-Loss Experience Rating Scheme for Fleets of Cars. Insurance: Mathematics and Economics, North-Holland, 173–179.Google Scholar
Winter, R. (2000) Optimal Insurance under Moral Hazard. In Handbook of Insurance (ed. Dionne, G.), Kluwer Academic Publishers, Boston, 155–184.CrossRefGoogle Scholar