基于分类风险模型的最优奖惩系统设计及在特定疾病保险中的应用

目的探讨不同索赔频率的分类风险模型的最优奖惩系统设计,并以糖尿病住院医疗保险实例予以验证。方法以2002年6月1日至2003年5年30日保险年度广州市居民因患糖尿病而住院治疗的1611例作为参保人群;采用满额理赔制,定义最低理赔起付线为10000元;建立以伽玛分布为结构函数的分类风险模型,采用矩法估计分类风险模型参数;用期望值原理构造推算纯保费,将年龄与性别作为风险因素引入最优奖惩系统,并推算不同类别保单组合的后验保费。结果四类投保人和全部保单的理赔次数分布均服从负二项分布。全部保单的初始年度纯保费为2579元,如果某一位投保人在未来5年内都没有发生理赔,则他可以得到一个66．35％的折扣。四类保单的理赔次数方差分别为0．5544、0．5857、0．9081、0．6365,第三类表现出更大的不均匀性,故对投保人的奖惩更为严厉,其他三类保单的理赔次数方差比较接近,表现出较大的同质性与相对弱化的奖惩力度。结论本文建立了基于分类风险模型的最优奖惩系统,并设计出基于信度的经验费率系统,这一经验费率系统具有公平性、财务平衡性等优点,为保险公司开发体现高风险损失应承担高额保险费保险原则的新保险品种提供了思路和依据。

Development and Application of an Optimal Bonus-malus System Based on Classified Risk Model in the Practices of Diseases-pecific Insurance

Objective To develop an optimal bonus-malus system based on a classified risk model with diverse claim frequencies and tested it in examples with insurance of diabetes-related hospitalization. Methods Between June 1st 2002 and May 30th 2003,1 661 cases of hospitalized diabetes were included for study.An increment-covering policy was used and the minimum deduction was 10 000 Yuan.The study was conducted by setting up a classified risk model,using moment method to estimate the parameters of risk model.The expected value principle to compute the pure premium,introducing risk factors into the bonus-malus system to calculate the posteriori premium of varied policy-holders. Results The claim numbers in either groups of policy-holders or in overall policies followed a negative binomial distribution.Initial purei premium for overall policies was 2 579 Yuan.For any policy-holder with zero claim during the next 5 years,66.35% discount-off would be rewarded.The variances of claim number in the four groups were(0.554 4),(0.585 7),0.908 1 and 0.636 5,respectively.Group 3 showed considerable heterogeneity,with a more rigorous penalization imposed by the bonus-malus system,while groups 1,2 and 4 were more close in the variance of claim number,receiving less rigor.(Conclusion A bonus-malus) system of classified risk model is developed and credibility-based experience-rating method worked out,which provides a basis for generation of"high risk,high premium"insurance services.