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Optimal design of a bonus-malus system: linear relativities revisited

Published online by Cambridge University Press:  20 October 2015

Chong It Tan
Chong It Tan*
Affiliation:
Research School of Finance, Actuarial Studies & Statistics, Australian National University, Australia
*
*Correspondence to: Chong It Tan, Research School of Finance, Actuarial Studies & Statistics, Australian National University, Canberra, ACT 0200, Australia. Tel: +612 6125 5458; Fax: +612 6125 0087; E-mail: chongit.tan@anu.edu.au
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Abstract

In this paper, we revisit the determination of optimal relativities under the linear form of relativities that is more viable in designing a commercial bonus-malus system. We derive the analytical formulae for the optimal linear relativities subject to a financial balanced inequality constraint. We also numerically investigate the impact of different a priori risk classification towards the effectiveness of transition rules. Our results show that the a priori risk segmentation is not a sensitive factor for the effectiveness of transition rules. Furthermore, relative to the general relativities, we find that the restriction of linear relativities only produces a small amount of deterioration towards the numerical value of the optimised objective function.

Keywords

Bonus-malus systemLinear relativitiesTransition rulesA posteriori ratingA priori claim frequency
Type
Papers
Information
Annals of Actuarial Science , Volume 10 , Issue 1 , March 2016 , pp. 52 - 64
Copyright
© Institute and Faculty of Actuaries 2015 

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References

Baione, F., Levantesi, S. & Menzieti, M. (2002). The development of an optimal bonus-malus system in a competitive market. ASTIN Bulletin, 32(1), 159–170.Google Scholar
Coene, G. & Doray, L.G. (1996). A financially balanced bonus-malus system. ASTIN Bulletin, 26(1), 107–116.Google Scholar
De Jong, P. & Heller, G.Z. (2008). Generalized Linear Models for Insurance Data. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Denuit, M., Maréchal, X., Pitrebois, S. & Walhin, J.-F. (2007). Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems. John Wiley & Sons, Chichester.Google Scholar
Dionne, G. & Vanasse, C. (1989). A generalization of actuarial automobile insurance rating models: the negative binomial distribution with a regression component. ASTIN Bulletin, 19(2), 199–212.CrossRefGoogle Scholar
Gilde, V. & Sundt, B. (1989). On bonus systems with credibility scales. Scandinavian Actuarial Journal, 1989(1), 13–22.Google Scholar
Lemaire, J. (1995). Bonus-Malus Systems in Automobile Insurance. Kluwer Academic Publishers, Boston, MA.Google Scholar
Lemaire, J., Park, S. & Wang, K. (2015). The impact of covariates on a bonus-malus system: an application of Taylor’s model. European Actuarial Journal, 5(1), 1–10.Google Scholar
McCullagh, P. & Nelder, J.A. (1989). Generalized Linear Models, 2nd ed. Chapman and Hall, London.CrossRefGoogle Scholar
Norberg, R. (1976). A credibility theory for automobile bonus system. Scandinavian Actuarial Journal, 1976(2), 92–107.Google Scholar
Pitrebois, S., Denuit, M. & Walhin, J.-F. (2003). Setting a bonus-malus scale in the presence of other rating factors: Taylor’s work revisited. ASTIN Bulletin, 33(2), 419–436.CrossRefGoogle Scholar
Pitrebois, S., Denuit, M. & Walhin, J.-F. (2004). Bonus-malus scales in segmented tariffs: Gilde & Sundt’s work revisited. Australian Actuarial Journal, 10(1), 107–125.Google Scholar
Tan, C.I., Li, J., Li, J.S.-H. & Balasooriya, U. (2015). Optimal relativities and transition rules of a bonus-malus system. Insurance: Mathematics and Economics, 61, 255–263.Google Scholar
Taylor, G. (1997). Setting a bonus-malus scale in the presence of other rating factors. ASTIN Bulletin, 27(2), 319–327.Google Scholar
Yip, K.C.H. & Yau, K.K.W. (2005). On modeling claim frequency data in general insurance with extra zeros. Insurance: Mathematics and Economics, 36(2), 153–163.Google Scholar