基于广义可加模型的汽车保险定价研究

发布时间：2018-06-02 04:25

本文选题：广义可加模型 + 惩罚最小二乘法　；参考：《浙江工商大学》2017年硕士论文

【摘要】：我国自1980年恢复机动车保险业务以来,车险业务飞速发展,在1988年其保费收入跃居财产保险收入第一位并一直占据榜首至今。但与保费收入发展不协调的是其赔付率,多数年份的赔付率超50%,赔付率过大导致保险公司一直未获利。因此,如何合理对车险产品定价,从而使公司获利,成为精算师们关注的问题。广义线性模型在车险定价研究的应用由来已久,其原理是假设所有协变量对响应变量函数的影响为预测函数的线性形式,但在实际的情况下,许多对索屶额的影响因素不仅仅是表现成线性形式的,单纯地用线性估计会造成一些变量的不显著而丢失重要影响因素。为了更好的拟合数据,必须对模型进行优化推广,在广义线性模型中纳入非参数预测项,将其推广到广义可加模型,从线性和非线性两个方面去分析各因素对响应变量函数不同的影响程度。本文首先对我国机动车保险业务的发展现状进行分析,然后利用惩罚最小二乘法和贝叶斯方法两种估计方法对广义可加模型的参数及非参数分别进行估计推导,并对我国某保险公司2015年的汽车保单损失数据,构建零调整伽玛模型(即零调整伽玛分布的广义可加模型),从"人、车和地区"等不同的因素去分析对索赔额的影响,最后通过拟合优度检验与广义线性模型进行对比。研究表明:由于车险保单不出险的概率极高,即索赔额在零点堆积,所以用零调整伽玛分布拟合我国机动车索赔额比指数分布族中常用的分布更适合,而将车身价值和车主年龄这两个协变量作为非线性影响因子建立广义可加模型比广义线性模型更具有优势,即广义可加模型更适用一般情形,具有更宽广的研究前景。
[Abstract]:Since the resumption of motor vehicle insurance business in China in 1980, the auto insurance business has developed rapidly. In 1988, the premium income of China has leapt to the first place in property insurance income and has occupied the first place ever since. But what is not in harmony with the development of premium income is its loss rate, which is over 50% in most years, and the loss rate is too large that the insurance company has never made a profit. Therefore, how to reasonably price the auto insurance products and make the company profit has become the concern of actuaries. The generalized linear model has long been applied in the study of vehicle insurance pricing. Its principle is to assume that the influence of all covariables on the response variable function is the linear form of the predictive function, but in the actual case, Many factors affecting the amount of suture are not only expressed in linear form, but simply used in linear estimation will cause some variables to be inconspicuous and lose important influence factors. In order to fit the data better, it is necessary to optimize and generalize the model, including the nonparametric prediction term in the generalized linear model, and extend it to the generalized additive model. The influence of different factors on the response variable function is analyzed from the linear and nonlinear aspects. In this paper, the current situation of motor vehicle insurance business in China is analyzed, and then the parameters and non-parameters of the generalized additive model are estimated by using the penalty least square method and Bayesian method, respectively. On the basis of the data of insurance policy loss of a certain insurance company in China in 2015, a zero-adjusted gamma model (that is, the generalized additive model of zero-adjusted gamma distribution) is constructed to analyze the influence of different factors such as "person, car and area" on the amount of claim. Finally, the goodness of fit test is compared with the generalized linear model. The research shows that because the probability of vehicle insurance policy is very high, that is, the amount of claim accumulates at zero point, it is more suitable to fit the amount of motor vehicle claim in our country with zero adjusted gamma distribution than the distribution commonly used in exponential distribution family. The generalized additive model is more advantageous than the generalized linear model, that is, the generalized additive model is more suitable for the general case and has a wider research prospect.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F842.634

【参考文献】