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1、分类号 F224 密级U D C 编号 10736硕 士 学 位 论 文基于个体索赔模型的未决赔款准备金估计研 究 生 姓 名 ： 张 兵 强指 导 教 师 姓 名 、 职 称 ： 陶 菊 春 教 授专 业 名 称 ： 概 率 论 与 数 理 统 计研 究 方 向 ： 应 用 统 计二 一 三 年 五 月The Estimation of Outstanding Claims Reserving onthe Individual Claims Loss ModelsBingqiang Zhang西 北 师 范 大 学 研究 生 学 位 论 文 作者 信 息论 文 题 目 基 于 个 体 索 赔
2、 模 型 的 未 决 赔 款 准 备 金 估 计姓 名 张 兵 强 学 号 2010210777专 业 名 称 概 率 论 与 数 理 统 计 答 辩 日 期 2013.05.22联 系 电 话 E_mail通 信 地 址 (邮 编 )：备 注 ：8 iAbstract ii1 1 X 11.1 9 . . . . . . . . . . . . . . . . . . . . . . 11.2 yG . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 M#? . . . . . . . . . . . . . . . . .
3、. . . . . . 31.4 SNS . . . . . . . . . . . . . . . . . . . . . . . 31 2 O 7 ; 52.1 F . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 G . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 B-F . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 3 . 133.1 ( . . . . . . . .
4、. . . . . . . . . . . . . . . . . . . 133.2 O 7? . . . . . . . . . . . . . . . . . . . . . . . . 1453.3 . . . . . . . . . . . . . . . . . . . . . . . . . 173.4 b . . . . . . . . . . . . . . . . . . . . . . . 173.5 O . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.6 RBNS IBNR . . . . . . .
5、. . . . . . . . . . . . . . 221 4 1 5 (z252931amuL 3537 xi5 , n J I?O 7 xi E xi+kX- . , O 7 O(5N xiE J : , iE+n?1 : ; , , O 7J 5 xiGUGxG )-K . x u) ? , I?O 7 I?O 7! O 7 , I?O 7 , O 7 , lnl 3XJ: . 3Ac , U3 cS ?n . ,XI?x , k S ; q X x , 9 3c y , Y w .3xO 7 , O 7 c5u6n/E F! B-F!Y . .u , YN o , ” N &E ,
6、 K O 7 O(5 . A O 7?1 O , SL 5 G . d , Xk /|8! n| , uy n A 9Cz5O 7 K .l Y 8 O 7?1 , LO Y w86n / , uN . , LT . r RBNSO 7 IBNRO 7m O . O 7 J # k c : O 7 ; IBNR; RBNS; iAbstractFor insurance companies, the scientic and reasonable extraction of the insuranceliability reserves is of great signicance to th
7、e protection of adequate solvency andstable development of the company. On the one hand, the reserve evaluation accuracyis an important aspect of assessment of insurance companies prots, and is also thefoundation of company management to scientic decision-making. On the other hand,the adequacy of pr
8、ovisioning the solvency of insurance company and risk conditionshave a signicant impact. According to the happening of insurance accident andthe claim progress of dierent pattern, liability reserve is divided into not incurredreserves and the outstanding claims reserve, the estimation of not incurre
9、d reservesis relatively straightforward, but the estimation of the outstanding claims reserve,whether in theory or from the method, there are a lot of diculties. Because usuallyin a specic years claim, claim often cant processed in the same year, especially forliability insurance that usually have a
10、 long legal process, its harm and cause of claimsusually appears within a few years later, these conditions can cause claim delay andreport delay.In non-life insurance reserves valuation practice, the primary method which in-surance companies used is deterministic models of the chain ladde and B-F m
11、ethod,these models are based on aggregate data, and usually produce inaccurate predictionsof the reserve because aggregated data usually failed to use all the information of theindividual claims. How to understand the historical observation data trends is thepremise of actuarial mathematics assessme
12、nt of liability reserves. In fact, the estima-tion of liability reserves of which we apply actuarial method is to predict the futurereparations situation according to the past experience. Therefore the key point is howto exploit past data eectively and nd the characteristics and trends of reparation
13、iimodel which it implied.We analysis the outstanding claims reserve from two aspects: the umber of claimamount and the compensation of claims, and set up a model on the individual claimloss, by increasing the ow of claim report number triangle. Through this model IBNRand RBNS claims can be separate
14、estimated, and provides a new eective method forreserve evaluation.Keywords: Claims reserves; IBNR; RBNS; Multinomial distribution.iii1 1 X 1.1 9g 1980cIEIS x 5 , x1 c k u ,-& J : ( ) F ; ( ) Y ; (n ) O 7? ; (o ) B F . 5 xiA , I ? n* . * O ”6n /eL 2.2ij 0 1 . j . n 2 n 11 z1,0 z1,1 . z1,j . z1,n2 z1,n12 z2,0 z2,1 . z2,j . z2,n2. . . .i zi,0 zi,1 . zi,j.n zn,0Table 2.2: O ”6n /O 7 O* O ”Zij, i + j n. =eO ”6n/ .2.1.3 O ” . O ” 5
