本文選題：廣義可加模型 + 懲罰最小二乘法　； 參考：《浙江工商大學(xué)》2017年碩士論文

【摘要】：我國自1980年恢復(fù)機(jī)動(dòng)車保險(xiǎn)業(yè)務(wù)以來,車險(xiǎn)業(yè)務(wù)飛速發(fā)展,在1988年其保費(fèi)收入躍居財(cái)產(chǎn)保險(xiǎn)收入第一位并一直占據(jù)榜首至今。但與保費(fèi)收入發(fā)展不協(xié)調(diào)的是其賠付率,多數(shù)年份的賠付率超50%,賠付率過大導(dǎo)致保險(xiǎn)公司一直未獲利。因此,如何合理對(duì)車險(xiǎn)產(chǎn)品定價(jià),從而使公司獲利,成為精算師們關(guān)注的問題。廣義線性模型在車險(xiǎn)定價(jià)研究的應(yīng)用由來已久,其原理是假設(shè)所有協(xié)變量對(duì)響應(yīng)變量函數(shù)的影響為預(yù)測(cè)函數(shù)的線性形式,但在實(shí)際的情況下,許多對(duì)索屶額的影響因素不僅僅是表現(xiàn)成線性形式的,單純地用線性估計(jì)會(huì)造成一些變量的不顯著而丟失重要影響因素。為了更好的擬合數(shù)據(jù),必須對(duì)模型進(jìn)行優(yōu)化推廣,在廣義線性模型中納入非參數(shù)預(yù)測(cè)項(xiàng),將其推廣到廣義可加模型,從線性和非線性兩個(gè)方面去分析各因素對(duì)響應(yīng)變量函數(shù)不同的影響程度。本文首先對(duì)我國機(jī)動(dòng)車保險(xiǎn)業(yè)務(wù)的發(fā)展現(xiàn)狀進(jìn)行分析,然后利用懲罰最小二乘法和貝葉斯方法兩種估計(jì)方法對(duì)廣義可加模型的參數(shù)及非參數(shù)分別進(jìn)行估計(jì)推導(dǎo),并對(duì)我國某保險(xiǎn)公司2015年的汽車保單損失數(shù)據(jù),構(gòu)建零調(diào)整伽瑪模型(即零調(diào)整伽瑪分布的廣義可加模型),從"人、車和地區(qū)"等不同的因素去分析對(duì)索賠額的影響,最后通過擬合優(yōu)度檢驗(yàn)與廣義線性模型進(jìn)行對(duì)比。研究表明:由于車險(xiǎn)保單不出險(xiǎn)的概率極高,即索賠額在零點(diǎn)堆積,所以用零調(diào)整伽瑪分布擬合我國機(jī)動(dòng)車索賠額比指數(shù)分布族中常用的分布更適合,而將車身價(jià)值和車主年齡這兩個(gè)協(xié)變量作為非線性影響因子建立廣義可加模型比廣義線性模型更具有優(yōu)勢(shì),即廣義可加模型更適用一般情形,具有更寬廣的研究前景。
[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.
【學(xué)位授予單位】：浙江工商大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224;F842.634

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