索赔次数与索赔额相依情形下的费率厘定研究

发布时间：2018-01-17 17:25

本文关键词：索赔次数与索赔额相依情形下的费率厘定研究　出处：《华东师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：传统分类费率厘定模型都是基于索赔次数与索赔额相互独立这一假设,但在实际中,索赔次数与索赔额通常是相关的。于是在本文中我们考虑索赔次数与索赔额相依情形下的费率厘定研究。在实际中,给定时间内同一个保单持有人多次的索赔额并不是相互独立的,因此我们在研究索赔次数与索赔额相关联的同时,用广义线性混合模型对索赔额进行建模。另外,我们假设不同保单持有人的索赔次数是相互独立的,用广义线性模型对其进行拟合。并在广义线性混合模型中将索赔次数作为解释变量来明确表现出索赔次数与索赔额的相关性,使得费率厘定的方法更加符合实际情况。我们采用基于EM算法的极大似然估计方法对广义线性混合模型以及广义线性模型中的参数进行估计。具体来说,我们用MH抽样方法构造了一个平稳分布为目标分布的马氏链,并对EM算法中的期望进行Monte Carlo近似。为消除随机性,我们对100个数据集进行参数估计。为了凸显考虑索赔额与索赔次数相关性的必要性,我们将上述模型的结果与二者独立情形下的传统费率结果进行比较,我们发现当二者为负相关时,相依情形下的净保费低于独立情形下的净保费,而二者为正相关时,相依情形下的净保费高于独立情形下的净保费。因此在费率厘定中考虑索赔次数与索赔金额之间的相关性是非常重要的。
[Abstract]:The traditional classification rate determination models are based on the hypothesis that the number of claims is independent of the amount claimed, but in practice. The number of claims is usually related to the amount claimed. So in this paper we consider the number of claims and the amount of claim in the case of the rate determination study. In practice. The amount claimed by the same policy holder multiple times within a given time is not independent of each other, so we are studying the correlation between the number of claims and the amount claimed. In addition, we assume that the number of claims for different policy holders is independent of each other. The generalized linear model is used to fit it, and the number of claims is taken as the explanatory variable in the generalized linear mixed model to show the correlation between the number of claims and the amount of claim. We use the maximum likelihood estimation method based on EM algorithm to estimate the parameters of generalized linear mixed model and generalized linear model. We construct a Markov chain with stationary distribution as target distribution by using MH sampling method, and apply Monte Carlo approximation to the expectation in EM algorithm to eliminate randomness. We estimate the parameters of 100 data sets. In order to highlight the need to consider the correlation between the amount of claims and the number of claims, we compare the results of the above model with the traditional rate results in the case of two independent cases. We find that when the two are negatively correlated, the net premium in the dependent case is lower than that in the independent case, while the two are positively correlated. The net premium in the dependent case is higher than that in the independent case, so it is very important to consider the correlation between the number of claims and the amount claimed in the rate determination.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F840

【参考文献】