基于修正负二项分布的索赔次数模型研究

发布时间：2018-01-30 21:50

本文关键词： 保险负二项分布 Probit函数零膨胀模型 Hurdle模型　出处：《重庆大学》2015年硕士论文　论文类型：学位论文

【摘要】：在自然、社会科学的计数资料的实际研究中,有一类特殊的计数数据:观察事件发生数中含有大量的零值,这种现象称之为零膨胀现象。此时,由于零事件所占比例过高,超出了传统模型的预测能力,若再应用传统的索赔次数模型如泊松模型、负二项模型就会导致模型的参数估计结果与真实值偏差过大,不能准确的预测损失次数。在这种情况下,Johnson和Kotz(1969)提出了零膨胀模型,Mullay(1986)在此基础上提出了另一种解决零膨胀现象的模型——Hurdle模型。这两种模型对零膨胀现象的研究提供了很好的研究思路。负二项分布对非同质风险的良好描述,使得其在风险管理中被广泛应用。Probit函数由于其具有的正态性也被广泛应用于各个领域。本文以负二项分布为基础,Probit函数为联接函数,研究了PNB-Hurdle模型和ZINB模型,并进一步建立了修正结构零的PC-ZINB模型。同时对模型进行了随机模拟试验,发现它们在对零膨胀数据进行拟合时,效果优于传统的计数数据模型。随着中国经济的蓬勃发展,保险行业在中国的增速不断加快,特别是非寿险行业中的汽车保险,已经成为了保险中最大份额的占有者,汽车保险的发展,关系着保险公司的存亡。因此,对汽车保险的研究很有意义。在此背景下,本文结合汽车保险的实际索赔数据,分别用泊松模型、负二项模型、PNB-Hurdle模型、GLNB模型、ZINB模型和PC-ZINB模型对数据进行参数估计和索赔次数预测,结果说明:由于数据表现出来的非同质性,使得经典的泊松模型失去了应有的模拟效果。传统的负二项模型虽然能够解决非同质性的问题,但是由于零膨胀现象的存在,其模拟效果也不是很好。同样的,广义负二项模型虽然可以解释影响因素,但零膨胀问题也使得它的拟合效果变差。PNB-Hurdle模型虽然可以解决零膨胀问题,但就本组数据来说,它的拟合效果并没有表现出它应有的优势。相对的,零膨胀模型在实证分析过程中展现出了良好的模拟效果,特别是PC-ZINB模型,其对零点的修正几乎完美,很好的解决了零膨胀现象。因此,对于零膨胀数据来说,若零事件来源相对单一,则可以用相对简单的PNB-Hurdle模型进行描述;若结构零来源相对单一,则ZINB模型能够拥有良好的模拟效果;若结构零来源比较复杂且包含不同性质的影响因素,PC-ZINB模型会更加适合于模型的预测。并且,对于零膨胀模型来说,将结构零划分为客观结构零和主观结构零的想法是可行的,特别是对于汽车保险。
[Abstract]:In the practical study of the natural and social science counting data, there is a special kind of counting data: the number of observed events contains a large number of zero values, which is called zero expansion phenomenon. Because the proportion of zero events is too high, which is beyond the prediction ability of the traditional model, if the traditional claim number model such as Poisson model is applied again. The negative binomial model will cause the parameter estimation of the model to deviate too much from the real value, and the loss times can not be accurately predicted. In this case. Johnson and Kotz (1969) proposed a zero expansion model. Mullay 1986). On this basis, another model to solve the problem of zero expansion, Hurdle model, is proposed. These two models provide a good idea for the study of zero expansion. The negative binomial distribution is good for non-homogeneous risk. Good description. It is widely used in risk management. Probit function is also widely used in various fields because of its normality. In this paper, based on negative binomial distribution, probit function is used as join function. The PNB-Hurdle model and the ZINB model are studied, and the modified PC-ZINB model with zero structure is established. It is found that when they fit the zero expansion data, the effect is better than the traditional counting data model. With the rapid development of Chinese economy, the growth of insurance industry in China is accelerating. Especially in the non-life insurance industry, automobile insurance has become the largest share of the occupants of insurance, the development of automobile insurance, related to the survival of insurance companies. In this context, combining with the actual claim data of automobile insurance, we use Poisson model, negative binomial model and PNB-Hurdle model respectively. ZINB model and PC-ZINB model are used to estimate the parameters of the data and predict the number of claims. The results show that: because of the heterogeneity of the data. The traditional negative binomial model can solve the problem of non-homogeneity, but because of the existence of zero expansion, the simulation effect is not very good. Although the generalized negative binomial model can explain the influence factors, the zero expansion problem also makes its fitting effect worse. PNB-Hurdle model can solve the zero expansion problem, but for the data of this group. Compared with the zero expansion model, the zero expansion model shows a good simulation effect in the process of empirical analysis, especially the PC-ZINB model. Its correction to 00:00 is almost perfect, which solves the problem of zero expansion well. Therefore, for zero expansion data, the source of zero event is relatively single. It can be described by a relatively simple PNB-Hurdle model. If the structure zero source is relatively single, the ZINB model can have good simulation effect. The PC-ZINB model is more suitable for the prediction of the model if the structure zero source is more complex and contains different influencing factors. Moreover, for the zero expansion model, the PC-ZINB model is more suitable for the prediction of the model. It is feasible to divide structural zero into objective structure zero and subjective structure zero, especially for automobile insurance.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F840.63;F224

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