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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1 611例作为参保人群;采用满额理赔制,定义最低理赔起付线为10 000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2 579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0.554 4、0.585 7、0.908 1、0.636 5,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。
Objective To investigate the optimal rewards and punishments system of classification risk models with different claims frequency and validate the case of diabetes inpatient medical insurance. METHODS: A total of 1 611 cases of hospitalizations for Guangzhou residents with diabetes due to diabetes during the insurance year from June 1, 2002 to May 30, 2003 were enrolled as insured persons. With the full compensation system, the minimum payout line was defined as 10,000 yuan ; To establish a classification risk model with the gamma distribution as a structural function, and to estimate the classification risk model parameters by using the moment method; to construct a pure premium by using the expectation principle and to introduce age and gender as the risk factors into the optimal reward and punishment system, and to calculate different types of policy combinations After the premiums. Results The distribution of the number of claims of the four types of policyholders and all policies follows the negative binomial distribution. The initial annual pure premium of all policies is $ 2,579. If an insured person does not have any claims for the next five years, he can receive a discount of 66.35%. The variance of the number of claims in the four types of policies was 0.554 4,0.585 7,0.908 1,0.636 5 respectively. The third category showed greater inhomogeneity, so the rewards and penalties for the policyholders were more severe. The number of claims for the other three types of policies The variance is relatively close, showing greater homogeneity and relative weakening rewards and punishments. Conclusion This paper establishes the optimal rewards and punishments system based on classification risk model, and designs a empirical rate system based on reliability. This experience rate system has the advantages of fairness and financial balance, and provides a foundation for insurance companies to develop high-risk losses Should assume the principle of high premium insurance new insurance species provide ideas and basis.