Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-23T03:08:54.190Z Has data issue: false hasContentIssue false
  • English
  • Français

Computing Bonus–Malus Premiums under Partial Prior Information

Published online by Cambridge University Press:  10 June 2011

E. Gómez-Déniz ,
L. Bermúdez  and
I. Morillo
E. Gómez-Déniz
Affiliation:
Department of Quantitative Methods, University of Las Palmas de Gran Canaria, 35017–Las Palmas de Gran Canaria, Spain., Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The use of classical bonus–malus systems entails very high maluses and other problems which, during recent years, have been criticised by actuaries. To avoid these problems, new bonus–malus models have been developed. For instance, it is well known that the use of an exponential loss function reduces the differences between overcharges and undercharges, solving the problem of high maluses. In order to measure the sensitivity of the exponential bonus–malus system, and according to robust Bayesian analysis, we first model the structure function by specifying a subclass of the generalised moments class. We then examine the range of relativities for each prior. Finally, we illustrate our method with a numerical example based on real data.

Keywords

Bonus–MalusGeneralised Moment ClassBayesian RobustnessExponential PrinciplePoisson-Inverse Gaussian
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 11 , Issue 2 , 01 June 2005 , pp. 361 - 374
Copyright
Copyright © Institute and Faculty of Actuaries 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bermúdez, Ll., Denuit, M. & Dhaene, J. (2001). Exponential bonus–malus systems integrating a priori risk classification. Journal of Actuarial Practice, 9, 67–98.Google Scholar
Betrò, B., Ruggeri, F. & Meczarski, M. (1994). Robust Bayesian analysis under generalized moments conditions. Journal of Statistical Planning and Inference, 41, 257–266.CrossRefGoogle Scholar
Dionne, G. & Vanasse, C. (1992). Automobile insurance ratemaking in the presence of asymmetrical information. Journal of Applied Econometrics, 7, 149–165.CrossRefGoogle Scholar
Eichenauer, J., Lehn, J. & Rettig, S. (1988). A gamma–minimax result in credibility theory. Insurance: Mathematics & Economics, 7, 1, 49–57.Google Scholar
Gisler, A. (1996). Bonus–malus and tariff segmentation. Paper presented at the XXVIIth Astin colloquium.Google Scholar
Gomez, E., Hernandez, A. & Vazquez, F. (2001). Robust Bayesian premium principles in actuarial science. Journal of the Royal Statistical Society (The Statistician, Series D), 49, 2, 241–252.Google Scholar
Gomez, E., Perez, J., Hernandez, A. & Vazquez, F. (2002). Measuring sensitivity in a bonus–malus system. Insurance: Mathematics & Economics, 31, 1, 105–113.Google Scholar
Gustafson, P. (1996a). Local sensitivity of posterior expectations. The Annals of Statistics, 24, 1, 174–195.CrossRefGoogle Scholar
Gustafson, P. (1996b). Local sensitivity of inferences to prior marginals. Journal of the American Statistical Association, 91, 434, 774–781.CrossRefGoogle Scholar
Lemaire, J. (1979). How to define a bonus–malus system with an exponential utility function. Astin Bulletin, 10, 274–282.CrossRefGoogle Scholar
Makov, U. (1995). Loss robustness via Fisher-weighted squared errors loss function. Insurance: Mathematics & Economics, 16, 1, 1–6.Google Scholar
Meng, Y. & Whitmore, G. (1999). Accounting for individual over-dispersion in a bonus–malus automobile insurance system. Astin Bulletin, 29, 2, 327–337.Google Scholar
Moreno, E., Bertolino, F. & Racugno, W. (2003). Bayesian inference under partial prior information. Scandinavian Journal of Statistics, 39, 565–580.CrossRefGoogle Scholar
Morillo, I. & Bermúdez, Ll. (2003). Bonus–malus system using an exponential loss function with an Inverse Gaussian distribution. Insurance: Mathematics & Economics, 33, 49–57.Google Scholar
Ríos, S., Martín, J., Ríos, D. & Ruggeri, F. (1999). Bayesian forecasting for accident proneness evaluation. Scandinavian Actuarial Journal, 99, 134–156.Google Scholar
Sivaganesan, S. & Berger, J.O. (1989). Ranges of posterior measures for priors with unimodal contaminations. Annals of Statistics, 17, 2, 868–889.CrossRefGoogle Scholar
Tremblay, L. (1992). Using the Poisson inverse Gaussian in bonus–malus systems. Astin Bulletin, 22, 1, 97–106.CrossRefGoogle Scholar
Winkler, G. (2000). Moment sets of bell-shaped distributions: extreme points, extremal decomposition and Chebysheff inequalities. Math. Nachr, 215, 161–184.3.0.CO;2-A>CrossRefGoogle Scholar
Young, V. (1998). Robust Bayesian credibility using semiparametric models. Astin Bulletin, 28, 1, 187–203.CrossRefGoogle Scholar