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在团体健康保险中,同一份保单通常包含若干被保险人,被保险人之间相依的风险特征使得保单的赔付数据呈现出分层结构的特点。同时,保单的索赔次数和索赔强度通常存在一定的相依关系,这种相依关系对保险公司纯保费的厘定结果具有重要的影响。为了准确预测团体健康保险的纯保费,本文建立了相依风险的贝叶斯分层模型,该模型用伽马分布来描述索赔强度数据,用零截断泊松分布来描述索赔次数数据,分别在模型均值中引入共同的随机效应来描述赔付数据的分层特征和索赔次数与索赔强度之间的相依关系;最后借助贝叶斯HMC算法进行参数估计,并给出了团体保单的损失预测分布。本文将该方法运用到我国一组团体健康保险的损失数据并对保单累积损失进行预测。结果表明,相依风险的贝叶斯分层模型具有良好的应用价值。
In group health insurance, the same insurance policy usually includes several insured persons. The risk characteristics of the insured person depend on the insurance policy to make the claims data have a hierarchical structure. At the same time, there is usually a certain relationship between the number of policy claims and the strength of claims. Such dependence has an important influence on the determination of insurance premiums. In order to accurately predict the net premium of group health insurance, a Bayesian hierarchical model with risk-dependent is established in this paper. The model uses Gamma distribution to describe the claim strength data and the zero-cut Poisson distribution to describe the claim frequency data. The common stochastic effect is introduced into the means to describe the stratification of claim data and the relationship between the number of claims and the strength of claims. Finally, the Bayesian HMC algorithm is used to estimate the parameters and the distribution of the loss forecast of the group policy is given. This paper applies the method to a group of group health insurance loss data and predicts the cumulative loss of the policy. The results show that the Bayesian stratification model with dependence risk has a good application value.