Exponential bonus-malus systems integrating a priori risk classification

Bermudez, Lluis;Denuit, Michel;Dhaene, Jan
(2001) Journal of Actuarial Practice — Vol. 9, p. 84-112 (2001)

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Abstract
The paper contains a brief review of the bonus/malus ratemaking methodology found within the European community. It proceeds to explain how, under such systems, a priori and a posteriori ratemaking have to be integrated into a continuous risk evaluation mechanism. Loss functions that are applicable to the analysis are introduced. Methods that are developed in the paper are then shown by an example using a portfolio of business from a Spanish insurer. Vehicle power, driver age, and driving record are all combined together within the analysis. It is ultimately shown that the (pre-judged) good risks are already rewarded in their base premiums, and consequently require a smaller bonus (i.e. premium reduction) following an accident-free period than do the risks that had been pre-judged as bad risks.
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Bermudez, L., Denuit, M., & Dhaene, J. (2001). Exponential bonus-malus systems integrating a priori risk classification. Journal of Actuarial Practice, 9, 84-112. https://hdl.handle.net/2078.5/88447 (Original work published 2001)