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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: egomez@dmc.ulpgc.es
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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

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