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Accounting for Individual Over-Dispersion in a Bonus-Malus Automobile Insurance System

Published online by Cambridge University Press:  29 August 2014

Meng Shengwang ,
Yuan Wei  and
G.A. Whitmore
Meng Shengwang
Affiliation:
Department of Statistics Renmin University, Beijing, China
Yuan Wei
Affiliation:
Department of Statistics Renmin University, Beijing, China
G.A. Whitmore*
Affiliation:
Faculty of Management McGill University, Montreal, Canada
*
Faculty of Management McGill University, 1001 Sherbrooke Street West, Montreal, Quebec H3A 1G5, Canadae-mail:, whitmore@management.mcgill.catel: 514-398-4049 fax:, 514-398-3876
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Abstract

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Individual automobile insurance claims are characterized by over-dispersion relative to the Poisson model. In addition, claim propensities vary among individuals in any insurance portfolio. This paper presents a model which takes account of both characteristics. The model employs the negative-binomial distribution as the distribution for individual-level claims and a Pareto distribution as the distribution for claim propensities within the portfolio. The paper shows that the resulting model is tractable and has a number of attractive properties which make it suitable for this application. The fit of the model to actual claim numbers for automobile third party liability insurance is examined and found acceptable. Bayes theorem is then applied to this model to calculate illustrative optimal premiums under the Bonus-Malus System (BMS).

Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 29 , Issue 2 , November 1999 , pp. 327 - 337
Copyright
Copyright © International Actuarial Association 1999

References

Cited References

Klugman, Stuart, Panjer, Harry H. and Willmot, Gordon E. (1998). Loss Models: From Data to Decisions, John Wiley & Sons, Inc.Google Scholar
Lemaire, Jean (1995). Bonus-Malus Systems for Automobile Insurance, Kluwer Academic Publishers.CrossRefGoogle Scholar
Yan, Maosong (1989). Bayes Risk Decisions, Qinghua University Publishing House.Google Scholar