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In recent papers, Bonus-Malus Scales (BMS) estimated using data have been considered as an alternative to longitudinal data and hierarchical data approaches to model the dependence between different contracts for the same insured. Those papers, however, did not discuss in detail how to construct and understand BMS models, and many of the BMS's basic properties were not discussed. The first objective of this paper is to correct this situation by explaining the logic behind BMS models and by describing those properties. More particularly, we will explain how BMS models are linked with simple count regression models that have covariates associated with the past claims experience. This study could help actuaries to understand how and why they should use BMS models for experience rating. The second objective of this paper is to create artificial past claims history for each insured. This is done by combining recent panel data theory with BMS models. We show that this addition significantly improves the prediction capacity of the BMS and provides a temporary solution for insurers who do not have enough historical data. We apply the BMS model to real data from a major Canadian insurance company. Results are analysed deeply to identify specific aspects of the BMS model. [ABSTRACT FROM AUTHOR]

How to consider the a priori risks in experience-rating models has been questioned in the actuarial community for a long time. Classic past-claim-rating models, such as the Buhlmann–Straub credibility model, normalize the past experience of each insured before applying claim penalties. On the other hand, classic Bonus–Malus Scales (BMS) models generate the same surcharges and the same discounts for all insureds because the transition rules within the class system do not depend on the a priori risk. Despite the quality of prediction of the BMS models, this experience-rating model could appear unfair to many insureds and regulators because it does not recognize the initial risk of the insured. In this paper, we propose the creation of different BMSs for each type of insured using recursive partitioning methods. We apply this approach to real data for the farm insurance product of a major Canadian insurance company with widely varying sizes of insureds. Because the a priori risk can change over time, a study of the possible transitions between different BMS models is also performed. [ABSTRACT FROM AUTHOR]

In a deregulated insurance market, insurance carriers have an incentive to be innovative in their pricing decisions by segmenting their portfolios and designing new bonus-malus systems (BMS). This paper examines the evolution of market shares and claim frequencies in a two-company market, when one insurer breaks off the existing stability by introducing a super-discount class in its BMS. Several assumptions concerning policyholders and insurers behavior are tested. Diffusion theory is used to model the spread of the information concerning the new BMS among prospective customers. A wide variety of market outcomes results: one company may take over the market or the two may survive with equal or unequal market shares, each specializing in a specific niche of the market. Before engaging in an aggressive competitive behavior, insurers should consequently be reasonably confident in their assumptions concerning the reactions of their policyholders to the new BMS. [ABSTRACT FROM AUTHOR]