关键词: 商业车险, 累积索赔金额, 纵向数据, 奖惩系统

Abstract: Premium rate of Commercial auto insurance is composed of a priori rate and a posteriori rate. The priori rate is based on an insured vehicle's prior risk characteristics by applying generalized linear models, and the posteriori rate is based on the claim experience of the insured vehicle by applying the bonus-malus system (BMS) to adjust the prior rate. The generalized linear models for priori rate making include frequency models, severity models and aggregated claim amount models. The bonus-malus system in practice only adjusts the a priori rate through the number of claims of an insured vehicle, without considering the impact of the claim amount. Aggregated claim amount is the sum of the claim amount of the insured vehicle during the insurance period, including both the claim number information and the claim amount information. In this paper, a new bonus-malus system is established by using the aggregated claim amount of insured vehicles, and an inverse-Gaussian regression is applied to predict a prior premium. The maximum likelihood method is used to simultaneously estimate the priori rate and BMS coefficients under a linear constraint. The new BMS avoids the excess bonus or malus to the insured that is a main problem of traditional BMS, so may effectively improve the posteriori rate of the insured vehicle.

Key words: Commercial Auto-Insurance, Aggregated Claim Amount, Longitudinal Data, Bonus-Malus System