基于累积索赔金额的最优奖惩系统

Optimal Bonus-Malus System (BMS) Based on the Aggregated Claim Amount

商业汽车保险的费率可以分解为先验费率和后验费率。先验费率是基于被保险车辆的先验风险特征信息(如驾驶人的性别和年龄、车辆使用性质)应用广义线性模型厘定的费率,而后验费率是基于被保险车辆的索赔经验(如索赔次数)应用奖惩系统对先验费率进行调整而得到的费率。厘定先验费率常用的广义线性模型包括索赔频率模型、索赔强度模型和累积索赔金额模型。实际应用中的奖惩系统通常基于被保险车辆的经验索赔次数对先验费率进行调整,没有考虑索赔金额的影响,也没有考虑先验信息的影响,有可能造成重复性的奖励或惩罚。累积索赔金额是被保险车辆在保险期间的索赔金额之和,既包含索赔次数信息,也包含索赔金额信息,可以更加准确地揭示被保险车辆的索赔经验信息。本文应用被保险车辆多年期的纵向累积索赔金额数据建立了一种新的奖惩系统,应用零调整逆高斯回归模型厘定先验费率,并在线性约束下用极大似然法同时估计先验费率因子和奖惩系数,避免了传统奖惩系统对被保险人可能造成的重复性奖励或惩罚,有效改进了后验费率的厘定结果。

Premium rate of Commercial auto insurance is composed of a priori rate and a posteriori rate. The priori rate is based on an insured vebicle＇ 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.