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

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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.
Original languageEnglish
Pages (from-to)52-64
Number of pages13
JournalAnnals of Actuarial Science
Issue number1
Publication statusPublished - Mar 2016
Externally publishedYes


  • Bonus-malus system
  • Linear relativities
  • Transition rules
  • A posteriori rating
  • A priori claim frequency


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