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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: [email protected]
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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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