Optimal relativities and transition rules of a bonus-malus system
Tan, Chong It
Li, Johnny Siu-Hang
Date of Issue2015
College of Business (Nanyang Business School)
When a bonus–malus system with a single set of optimal relativities and a set of simple transition rules is implemented, two inadequacy scenarios are induced because all policyholders are subject to the same a posteriori premium relativities (level transitions) independent of their a priori characteristics (current levels occupied). In this paper we propose a new objective function in the determination of optimal relativities that directly incorporates the a priori expected claim frequencies to partially address one of the inadequacy scenarios. We derive the analytical solution for the optimal relativities under a financial equilibrium constraint. Furthermore, we introduce a metric called effectiveness of transition rules to compare the different specifications of transition rules. We also argue that varying transition rules which are more flexible in addressing the other inadequacy scenario may be more effective than their corresponding simple rules.
Insurance : mathematics and economics
© 2015 [Elsevier B.V.] This is the author created version of a work that has been peer reviewed and accepted for publication by [Insurance: Mathematics and Economics], [Elsevier B.V.]. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.insmatheco.2015.02.001].