R大全2\R案例集合\10-mengshengwang-actuarial-science

R在精算中的应用孟生旺中国人民大学统计学院http://blog.sina.com.cn/mengshw第5届中国R会议1概述统计精算寿险：定价、准备金、分类非寿险：定价、准备金、分类统计软件：R，SAS，……精算软件Prophet，MoSes，VIP,IGLOO,EMBlem2统计软件在非寿险精算中的应用SourcePalisade2006(@Risk):http://www.palisade.com/downloads/pdf/Pryor.pdf3EXCEL，SAS，R的简单比较EXCEL：简单易学，容易出错，结果不稳定，计算效率低，统计功能有限。SAS：大型数据，强大的统计 分析 定性数据统计分析pdf销售业绩分析模板建筑结构震害分析销售进度分析表京东商城竞争战略分析 功能。R：灵活性，扩展性，强大的统计计算和绘图功能……4精算应用中的R包利息理论和寿险精算：lifecontigencies损失模型：actuar非寿险准备金评估：ChainLadder非寿险定价：glm，glm.nb(在MASS包中）,cplm，gamlss数据处理和绘图：plyr，reshape，ggplot25利息理论与寿险精算：lifecontigencies功能：人口统计、利息理论和精算数学的计算寿险保单的定价、准备金评估不足：目前只能处理单减因 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 不能处理连续时间。Bug？6Lifecontigencies示例>library(lifecontingencies)>nominal2Real(i=0.12,k=12,type="interest")>#现值计算>cf=c(10,20,30)#现金流>t=1:3#付款时间>p=c(0.5,0.6,0.8)#付款概率>i=0.03#年实际利率>presentValue(cashFlows=cf,timeIds=t,interestRates=i,probabilities=p)[1]38.12892>#30岁，10年定期寿险，年利率4%>Axn(soa08Act,30,10,i=0.04)[1]0.015772837Abug？>library(lifecontingencies)>cf=c(10,10,10,10,10,110)>t=1:6>duration(cf,t,i=0.03,macaulay=F)#得到macaulay久期？[1]4.984214>sum(t*cf*1.03^(-t))/sum(cf*1.03^(-t))#直接计算macaulay久期[1]4.984214>convexity(cf,t,i=0.03)#计算凸度[1]30.69613>sum(t*(t+1)*cf*(1+0.03)^(-t-2))/sum(cf*1.03^(-t))直接计算凸度[1]30.696138损失模型：actuar分布计算和参数估计：d,p,q,r,m,lev信度模型累积损失的计算破产概率的计算分层损失模型的随机模拟注：CAS的LSM可以模拟保险公司的损失发生过程及其进展：http://www.casact.org/research/lsmwp/index.cfm?fa=software9Actuar：BS信度模型示例>library(actuar)>mydatapolicyloss1loss2loss3w1w2w31117381642179478619251870622136414081597162217421523331759168514791147135713294NANA1010NANA348>myfit=cm(~policy,mydata,ratios=loss1:loss3,weights=w1:w3)10>summary(myfit)Call:cm(formula=~policy,data=mydata,ratios=loss1:loss3,weights=w1:w3)StructureParametersEstimatorsCollectivepremium:1566.874Betweenpolicyvariance:24189.8Withinpolicyvariance:34611317DetailedpremiumsLevel:policypolicyIndiv.meanWeightCred.factorCred.premium11722.485258180.94749051714.31421452.29748870.77352601478.24631635.71838330.72817801617.00541010.0003480.19563501457.93011#分层信度模型>mydata1typepolicyloss1loss2loss3w1w2w31A11738164217947861925187062B21364140815971622174215233A31759168514791147135713294B4NANA1010NANA348>myfit1=cm(~type+type:policy,mydata1,ratios=loss1:loss3,weights=w1:w3,method='iterative')12>summary(myfit1)Call:cm(formula=~type+type:policy,data=mydata1,ratios=loss1:loss3,weights=w1:w3,method="iterative")StructureParametersEstimatorsCollectivepremium:1560.691Betweentypevariance:33970.18Withintype/Betweenpolicyvariance:5775.545Withinpolicyvariance:34611317DetailedpremiumsLevel:typetypeIndiv.meanWeightCred.factorCred.premiumA1694.3191.20171080.87605561677.757B1404.1390.50406690.74777941443.625Level:policytypepolicyIndiv.meanWeightCred.factorCred.premiumA11722.485258180.811612771714.059B21452.29748870.449183681447.520A31635.71838330.390097991661.358B41010.0003480.054883221419.82613Actuar：累积损失计算示例S=X1+X2+…+XNlibrary(actuar)fx=discretize(pgamma(x,2,1),from=0,to=22,step=0.5,method="unbiased",lev=levgamma(x,2,1))#单次损失分布的离散化Fs=aggregateDist("recursive",model.freq="poisson",model.sev=fx,lambda=10,x.scale=0.5)#累积损失的计算>VaR(Fs,seq(0.9,1,0.02))90%92%94%96%98%100%30.531.533.035.038.071.0>CTE(Fs,seq(0.9,1,0.02))90%92%94%96%98%100%35.4187436.3042237.6462639.4580842.21550NaN14par(mfrow=c(1,2))plot(Fs,verticals=T,do.points=F,col=2,main='分布函数')#分布函数plot(diff(Fs),type='l',col=2,main='密度函数')#密度函数15非寿险准备金评估：ChainLadder基于流量三角形适用于常见的准备金评估 方法 快递客服问题件处理详细方法山木方法pdf计算方法pdf华与华方法下载八字理论方法下载 ：确定性模型随机模型：bootstrap，GLM16Chainladder：基于GLM的准备金评估示例>datdevorigin12345678910198150182710911181135416181801186118661883198211429540106713791561156316301684NA1983341899138716141873222122862346NANA1984566115615772127234326092707NANANA19851099561583221625952617NANANANA1986151644117012931585NANANANANA19875640210951232NANANANANANA19881356951311NANANANANANANA1989313539NANANANANANANANA1990206NANANANANANANANANA>fit=glmReserve(dat,var.power=2,mse.method='bootstrap')1718Coefficients:EstimateStd.ErrortvaluePr(>|t|)(Intercept)5.43635570.320434416.966<2e-16***factor(origin)1982-0.18976760.3127652-0.6070.54783factor(origin)19830.09168300.32709770.2800.78086factor(origin)19840.31905450.34274450.9310.35812factor(origin)19850.15607110.36135160.4320.66838factor(origin)1986-0.16960000.3849454-0.4410.66215factor(origin)1987-0.35524830.4169667-0.8520.39986factor(origin)1988-0.00071450.4645266-0.0020.99878factor(origin)1989-0.09009730.5461889-0.1650.86990factor(origin)1990-0.10847950.7368022-0.1470.88377factor(dev)20.75107200.31276522.4010.02162*factor(dev)30.75654160.32709772.3130.02656*factor(dev)40.32152010.34274450.9380.35446factor(dev)50.15818250.36135160.4380.66418factor(dev)6-0.12443260.3849454-0.3230.74838factor(dev)7-1.06707760.4169667-2.5590.01484*factor(dev)8-1.25815270.4645266-2.7080.01028*factor(dev)9-1.87691950.5461889-3.4360.00150**factor(dev)10-2.60314240.7368022-3.5330.00115**19>fit$summaryLatestDev.To.DateUltimateIBNRS.ECV198216840.991755016981415.399441.0999601198323460.976279724035742.687830.7489093198427070.94353432869162102.596930.6333144198526170.91921322847230127.547430.5545540198615850.82466181922337193.093260.5729770198712320.72470591700468271.487800.5801021198813110.57124182295984563.303820.572463219895390.285790018861347890.468920.661075719902060.1048346196517591425.985890.8106799total142270.72642331958553581973.537460.368334720可以用于非寿险定价的R包glmglm.nbcplmgamlss21gamlss的应用示例拟合损失次数,数据来源：deJong(2008）>datclaimsfreq10632322143333227143185422223>library(gamlss)>fam=c('PO','NBI','NBII','PIG','DEL','SICHEL','ZIP','ZINBI')>m1=m2=list()>for(iin1:8){m1[[fam[i]]]=GAIC(gamlss(claims~1,weights=freq,data=dat,family=fam[i],n.cyc=100,trace=F))+m2[[fam[i]]]=GAIC(gamlss(claims~1,weights=freq,data=dat,family=fam[i],n.cyc=100,trace=F),k=log(sum(dat$freq)))}>sort(unlist(m1))#AIC比较PIGNBINBIISICHELDELZINBIZIPPO36102.9136103.3636103.3636104.9136104.9336105.6036108.4036205.00>sort(unlist(m2))#SBC比较PIGNBINBIIZIPSICHELDELZINBIPO36121.1636121.6136121.6136126.6536132.2836132.3036132.9736214.1324claimsfreqPIGPO106323263232.163094.32143334332.74590.632271270.9167.0431818.74.15421.40.125R与SAS在精算应用中的几个比较优化：R：optim，nlm……SAS：NLMIXEDGLM：R：glm，glm.nb,gamlssSAS：GENMODGLMM：R：lme4SAS：GLIMMIX，NLMIXED26小结R和SAS需要互补R的精算包：需要进一步完善和优化R对精算学习的影响27