本文關(guān)鍵詞：索賠次數(shù)與索賠額相依情形下的費(fèi)率厘定研究　出處：《華東師范大學(xué)》2017年碩士論文　論文類(lèi)型：學(xué)位論文

  更多相關(guān)文章： 索賠次數(shù) 索賠額 費(fèi)率厘定 GLM GLMM MCEM MH抽樣

【摘要】：傳統(tǒng)分類(lèi)費(fèi)率厘定模型都是基于索賠次數(shù)與索賠額相互獨(dú)立這一假設(shè),但在實(shí)際中,索賠次數(shù)與索賠額通常是相關(guān)的。于是在本文中我們考慮索賠次數(shù)與索賠額相依情形下的費(fèi)率厘定研究。在實(shí)際中,給定時(shí)間內(nèi)同一個(gè)保單持有人多次的索賠額并不是相互獨(dú)立的,因此我們?cè)谘芯克髻r次數(shù)與索賠額相關(guān)聯(lián)的同時(shí),用廣義線(xiàn)性混合模型對(duì)索賠額進(jìn)行建模。另外,我們假設(shè)不同保單持有人的索賠次數(shù)是相互獨(dú)立的,用廣義線(xiàn)性模型對(duì)其進(jìn)行擬合。并在廣義線(xiàn)性混合模型中將索賠次數(shù)作為解釋變量來(lái)明確表現(xiàn)出索賠次數(shù)與索賠額的相關(guān)性,使得費(fèi)率厘定的方法更加符合實(shí)際情況。我們采用基于EM算法的極大似然估計(jì)方法對(duì)廣義線(xiàn)性混合模型以及廣義線(xiàn)性模型中的參數(shù)進(jìn)行估計(jì)。具體來(lái)說(shuō),我們用MH抽樣方法構(gòu)造了一個(gè)平穩(wěn)分布為目標(biāo)分布的馬氏鏈,并對(duì)EM算法中的期望進(jìn)行Monte Carlo近似。為消除隨機(jī)性,我們對(duì)100個(gè)數(shù)據(jù)集進(jìn)行參數(shù)估計(jì)。為了凸顯考慮索賠額與索賠次數(shù)相關(guān)性的必要性,我們將上述模型的結(jié)果與二者獨(dú)立情形下的傳統(tǒng)費(fèi)率結(jié)果進(jìn)行比較,我們發(fā)現(xiàn)當(dāng)二者為負(fù)相關(guān)時(shí),相依情形下的凈保費(fèi)低于獨(dú)立情形下的凈保費(fèi),而二者為正相關(guān)時(shí),相依情形下的凈保費(fèi)高于獨(dú)立情形下的凈保費(fèi)。因此在費(fèi)率厘定中考慮索賠次數(shù)與索賠金額之間的相關(guān)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.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：F224;F840

【參考文獻(xiàn)】

相關(guān)期刊論文 前4條

1 張連增;孫維偉;;廣義線(xiàn)性混合模型在保險(xiǎn)索賠中的應(yīng)用及R實(shí)現(xiàn)[J];江西財(cái)經(jīng)大學(xué)學(xué)報(bào);2013年04期

2 羅妍;孟生旺;;非壽險(xiǎn)分類(lèi)費(fèi)率模型的比較研究和實(shí)證分析[J];數(shù)理統(tǒng)計(jì)與管理;2011年01期

3 孟生旺;;非壽險(xiǎn)分類(lèi)費(fèi)率模型及其參數(shù)估計(jì)[J];數(shù)理統(tǒng)計(jì)與管理;2007年04期

4 盧志義;劉樂(lè)平;;廣義線(xiàn)性模型在非壽險(xiǎn)精算中的應(yīng)用及其研究進(jìn)展[J];統(tǒng)計(jì)與信息論壇;2007年04期

相關(guān)碩士學(xué)位論文 前1條

1 姬文鴿;基于廣義線(xiàn)性混合模型的未決賠款準(zhǔn)備金估計(jì)方法研究[D];暨南大學(xué);2011年

，

本文編號(hào)：1437234