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车险费率厘定精算技术的研究与应用评述
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  • 英文篇名:Research and Application Review of Actuarial Techniques in Vehicle Insurance Ratemaking
  • 作者:孙维伟 ; 张连增
  • 英文作者:SUN Wei-wei;ZHANG Lian-zeng;School of Management,Tianjin University of Technology;Department of Risk Management and Insurance,School of Economics,Nankai University;
  • 关键词:车险 ; 费率厘定 ; 精算技术 ; 统计模型 ; 参数估计
  • 英文关键词:auto insurance;;ratemaking;;actuarial techniques;;statistical models;;parameter estimation
  • 中文刊名:SLTJ
  • 英文刊名:Journal of Applied Statistics and Management
  • 机构:天津理工大学管理学院;南开大学金融学院精算系;
  • 出版日期:2017-01-21 08:49
  • 出版单位:数理统计与管理
  • 年:2017
  • 期:v.36;No.208
  • 基金:国家自然科学基金青年项目(71603180)和面上项目(71271121)的资助
  • 语种:中文;
  • 页:SLTJ201702015
  • 页数:15
  • CN:02
  • ISSN:11-2242/O1
  • 分类号:140-154
摘要
精算技术为中国车险市场费率改革提供必要支持,可以确保费率厘定的科学性与合理性。首先,本文系统梳理了车险分类风险费率厘定精算统计模型的发展历程,并回顾参数估计方法。其次,论述了车险个体风险费率厘定的精算模型与方法,并重点评述了信度理论与奖惩系统的研究。进而,归纳出车险费率厘定精算统计模型的研究热点与发展方向。最后,指明现有研究对中国车险费率厘定精算方法的启示,并提出相关建议。
        Actuarial techniques provide the necessary support for rate reform of vehicle insurance market in China,which can ensure the accurateness and rationality of ratemaking.First of all,this paper runs through the development course of auto insurance classification ratemaking models,as well as estimation methods of their parameters.Secondly,the paper discusses the actuarial models and methods of auto insurance individual risk ratemaking,and focuses on the study of credibility theory and Bonus-Malus System.Furthermore,the paper sums up the research hotspot and future development of actuarial and statistical models on auto insurance ratemaking.At last,inspiration of existing research to actuarial models and methods of China's auto insurance ratemaking are pointed out,as well as recommendations are made.
引文
[1]McCullagh P,Nelder J A.Generalized Linear Models(2nd ed.)[M].New York:Chapman and Hall/CRC,1989.
    [2]de Jong P,Heller G Z.Generalized Linear Models for Insurance Data[M].New York:United States of America by Cambridge University Press,2008.
    [3]Ohlsson E.Combining generalized linear models and credibility models in practice[J].Scandinavian Actuarial Journal,2008,4:301-314.
    [4]Ohlsson E,Johansson B.Non-life Insurance Pricing with Generalized Linear Models[M].Berlin:Springer-Verlag,2010.
    [5]毛泽春,刘锦萼.广义线性模型与保费点数计价系统[J].统计研究,2002,(6):23-27.
    [6]卢志义,刘乐平.广义线性模型在非寿险精算中的应用及其研究进展[J].统计与信息论坛,2007,22(4):26-31.
    [7]孟生旺.非寿险分类费率模型及其参数估计[J].数理统计与管理,2007,26(4):584-588.
    [8]孟生旺.广义线性模型在汽车保险定价的应用[J].数理统计与管理,2007,26(1):24-29.
    [9]钟桢,孟生旺.基于伽玛与对数正态分布假设下的广义线性模型的比较和应用[J].数理统计与管理,2010,29(3):430-436.
    [10]罗妍,孟生旺.非寿险分类费率模型的比较研究和实证分析[J].数理统计与管理,2011,30(1):162-168.
    [11]张连增,吕定海.广义线性模型在非寿险费率分析中的应用[J].数理统计与管理,2013,32(5):903-909.
    [12]王慧萍.我国机动车辆保险分类费率厘定的实证研究[D].长沙:湖南大学,2005.
    [13]陈福生.广义线性模型及其在车辆损失保险精算中的应用[D].上海:复旦大学,2006.
    [14]张茵.对加入从人因素的我国车险费率厘定的研究[D].长沙:湖南大学,2007.
    [15]汪云霞.基于广义线性模型的保险风险识别和定价[D].合肥:中国科学技术大学,2008.
    [16]郝红红.基于GLM的我国车险费率厘定的实证研究[D].天津:天津财经大学,2010.
    [17]牛睿尧.基于广义线性模型的机动车险分类费率厘定方法研究[D].吉林:吉林大学,2011.
    [18]孟生旺.神经网络模型与车险索赔频率预测[J].统计研究,2012,29(3):22-26.
    [19]Hastie T,Tibshirani R.Generalized additive models[J].Statistical Science,1986,1(3):297-318.
    [20]Hastie T,Tibshirani R.Generalized Additive Models[M].London:Chapman and Hall/CRC,1990.
    [21]Hastie T,Tibshirani R.Varying-coefficient models[J].Journal of the Royal Statistical Society(Series B),1993,55(4):757-796.
    [22]Guisan A,Edwards T C,Hastie T.Generalized linear and generalized additive models in studies of species distributions:setting the scene[J].Ecological modeling,2002,157:89-100.
    [23]Wood S N.Generalized Additive Models:An Introduction with R[M].Boca Raton:Chapman&Hall/CRC,2006.
    [24]Greaves G J,Mathieu G R,Seddon P J.Predictive modeling and ground validation of the spatial distribution of the New Zealand long-tailed bat(Chalinolobus Tuberculatus)[J].Biological Conservation,2006,132:211-221.
    [25]童丽娟.GAM在汽车保险定价中的应用研究[D].湖南:湖南大学,2010.
    [26]童丽娟.GAM在汽车保险定价中的应用研究[J].数学的实践与认识,2011,41(17):64-69.
    [27]张连增,孙维伟,段白鸽.GLM与GAM在车险索赔频率建模中的应用及其比较[J].现代财经,2012,32(12):47-56.
    [28]Antonio K,Beirlant J.Issues in claims reserving and credibility:A semiparametric approach with mixed models[J].Journal of Risk and Insurance,2008,75(3):643-676.
    [29]Yau K,Yip K,Yuen H K.Modeling repeated insurance claim frequency data using the generalized linear mixed model[J].Journal of Applied Statistics,2003,30(8):857-865.
    [30]Antonio K,Beirlant J.Actuarial statistics with generalized linear mixed models[J].Insurance:Mathematics and Economics,2007,40(1):58-76.
    [31]Frees E W,Valdez E A.Hierarchical insurance claims modeling[J].Journal of the American Statistical Association,2008,103(484):1457-1469.
    [32]Antonio K,Frees E W,Valdez E A.A Multilevel analysis of intercompany claim counts[J].ASTIN Bulletin,2010,40(1):151-177.
    [33]孟生旺,邱子真.混合效应模型及其在非寿险费率厘定中的应用[J].数理统计与管理,2016,35(1):154-161.
    [34]Lee Y,Nelder J.Hierarchical generalized linear models[J].Journal of the Royal Statistical Society B,1996,58:619-678.
    [35]段白鸽,张连增.分层模型在非寿险精算学中的应用研究评述[J].统计研究,2013,30(5):98-105.
    [36]Bailey R A,Simon L J.Two studies in automobile insurance ratemaking[J].ASTIN Bulletin,1960,1(4):192-217.
    [37]Bailey R A.Insurance rates with minimum bias[J].Proceedings of the Casualty Actuarial Society,1963:4-11.
    [38]Jung J S.On automobile insurance ratemaking[J].ASTIN Bulletin,1966,1(5):41-48.
    [39]Ajne B.A note on the multiplicative ratemaking model[J].ASTIN Bulletin,1975,8(2):144-153.
    [40]Chamberlain C E.Relativity pricing through analysis of variance[J].Discussion Paper Program of the Casualty Actuarial Society,1980:4-24.
    [41]Fu L,Wu C S P.General iteration algorithm for classification ratemaking[J].Variance Casualty Actuarial Society-Arlington,Virginia,2007,1(02):193-213.
    [42]Dobson A J,Barnett A.An Introduction to Generalized Linear Models[M].London:Chapman and Hall,2008.
    [43]孟生旺.汽车保险的精算统计模型[M].北京:中国统计出版社,2014.
    [44]Breslow N E,Clayton D G.Approximate inference in generalized linear mixed models[J].Journal of the American Statistical Association,1993,88(421):9-25.
    [45]McGilchrist C A.Estimation in generalized mixed models[J].Journal of the Royal Statistical Society(Series B),1994,56:61-69.
    [46]Lee Y,Nelder J A.Double Hierarchical generalized linear models(with discussion)[J].Journal of the Royal Statistical Society(Series C),2006,55(2):139-185.
    [47]Liang K Y,Zeger S L.Longitudinal data analysis using generalized linear models[J].Biometrika,1986,73(1):13-22.
    [48]Lee Y,Nelder J A,Pawitan Y.Generalized Linear Models with Random Effects:Unified Analysis via h-Likelihood[M].Boca Raton:Chapman and Hall/CRC,2006.
    [49]刘乐平,高磊,卢志义.贝叶斯身世之谜—写在贝叶斯定理发表250周年之际[J].统计研究,2013,30(12):3-9.
    [50]Dey D,Ghosh S,Mallick B.Generalized Linear Models:A Bayesian Perspective[M].New York:Marcel Dekker,2000.
    [51]Ntzoufras I.Beyesian Modeling Using WinBUGS[M].Hoboken:John Wiley&Sons,2009.
    [52]Fuzi M F M,Jemain A A,Ismail N.Bayesian quantile regression model for claim count data[J].Insurance:Mathematics and Economics,2016,66:124-137.
    [53]Fahrmeir L,Lang S.Bayesian inference for generalized additive mixed models based on Markov random field priors[J].Journal of the Royal Statistical Society(Series C),2001,50(2):201-220.
    [54]Denuita M,Langb S.Non-life rate-making with Bayesian GAMs[J].Insurance:Mathematics and Economics,2004,35(3):627-647.
    [55]Klein N,Denuit M,Lang S,et al.Nonlife ratemaking and risk management with Bayesian generalized additive models for location,scale,and shape[J].Insurance:Mathematics and Economics,2014,55(1):225-249.
    [56]Zeger S L,Karim M R.Generalized linear models with random effects:A Gibbs sampling approach[J].Journal of the American Statistical Association,1991,86(413):79-86.
    [57]Zhao Y,Staudenmayer J,Coull B A,et al.General design Bayesian generalized linear mixed models[J].Statistical Science,2006,21(1):35-51.
    [58]Scollnik D R M.Actuarial modeling with MCMC and BUGs[J].North American Actuarial Journal,2001,5(2):96-124.
    [59]Jewell W S.The use of collateral data in credibility theory:A hierarchical model[J].Giornale dell'Instituto Italiano degli Attuari,1975,38:1-16.
    [60]Sundt B.A multi-level hierarchical credibility regression model[J].Scandinavian Actuarial Journal,1980,1980(1):25-32.
    [61]Sundt B.Two credibility regression approaches for the classification of passenger cars in a multiplicative tariff[J].ASTIN Bulletin,1987,17(1):42-70.
    [62]Nelder J A,Verrall R J.Credibility theory and generalized linear models[J].ASTIN Bulletin,1997,27(1):71-82.
    [63]Kaas R,Goovaerts M,Dhaene J,et al.Modern Actuarial Risk Theory:Using R[M].Berlin:Springer Science&Business Media,2008.
    [64]谢远涛,李政宵.基于联合定价模型的奖惩因子的扩展与比较[J].统计与信息论坛,2015,30(6):33-39.
    [65]贺宝龙.广义线性混合模型在精算分析中的应用[D].湖北:武汉理工大学,2008.
    [66]康萌萌.基于广义线性混合模型的经验费率厘定[J].统计与信息论坛,2009,24(7):51-56.
    [67]Klinker F.Generalized linear mixed models for ratemaking:A means of introducing credibility into a generalized linear model setting[R].Casualty Actuarial Society E-Forum,2011,2:1-25.
    [68]谢远涛,王稳,谭英平,杨娟.广义线性混合模型框架下的信度模型分析[J].统计与信息论坛,2012,27(10):3-8.
    [69]康萌萌,孟生旺.基于MCMC模拟和伪似然估计法的交叉分类信度模型费率厘定[J].统计与信息论坛,2014,29(2):34-39.
    [70]孟生旺,肖展航.基于偏正态随机效应模型的信度保费[J].统计研究,2015,32(1):73-78.
    [71]刘乐平,袁卫.现代Bayes方法在精算学中的应用及展望[J].统计研究,2002,(8):45-49.
    [72]朱慧明,郝立亚.非寿险精算中的贝叶斯信用模型分析[J].数量经济技术经济研究,2007,(1):109-117.
    [73]Lemaire J.Bonus-Malus Systems in Automobile Insurance[M].Boston:Kluwer Academic Publishers,1995.
    [74]Lemaire J.Bonus-Malus Systems:The European and Asian approach to Merit-rating[J].North American Actuarial Journal,1998,2(1):26-47.
    [75]Frangos N E,Vrontos S D.Design of optimal Bonus-Malus Systems with a frequency and a severity component on an individual basis in automobile insurance[J].ASTIN Bulletin,2001,31(1):1-22.
    [76]Brouhns N,Guillen M,Pinquet J.Bonus-malus scales in segmented tariffs with stochastic migration between segments[J].The Journal of Risk and Insurance,2003,70(4):577-599.
    [77]孟生旺.保险定价:经验估费系统研究[D].北京:中国人民大学,1998.
    [78]Najafabadi A T P,Dizaji A K.A dynamic Bonus-Malus system for the automobile insurance:A case study in iranian third party liability[J].IUP Journal of Risk and Insurance,2011,8(3):37.
    [79]孟生旺.考虑个体保单风险特征的最优奖惩系统[J].数理统计与管理,2013,32(3):505-510.
    [80]Mahmoudvand R,Hassani H.Generalized bonus-malus systems with a frequency and a severity component on an individual basis in automobile insurance[J].ASTIN Bulletin,2009,39(1):307-315.
    [81]Tzougas G,Vrontos S,Frangos N.Optimal bonus-malus systems using finite mixture models[J].ASTIN Bulletin,2014,44(2):417-444.
    [82]Tan C I,Li J,Li J S H,et al.Optimal relativities and transition rules of a bonus-malus system[J].Insurance:Mathematics and Economics,2015,61:255-263.
    [83]Tan C I.Optimal design of a bonus-malus system:linear relativities revisited[J].Annals of Actuarial Science,2016,10(1):52-64.
    [84]Rigby R A,Stasinopoulos D M.Generalized additive models for location,scale and shape[J].Applied Statistics,2005,54(3):507-554.
    [85]Heller G Z,Stasinopoulos D M,Rigby R A.The zero-adjusted inverse Gaussian distribution as a model for insurance data[J].Proceedings of the International Workshop on Statistical Modeling,Galway,2006,226-233.
    [86]Heller G Z,Stasinopoulos D M,Rigby R A,et al.Mean and dispersion modelling for policy claims costs[J].Scandinavian Actuarial Journal.2007,4:281-292.
    [87]徐昕,袁卫,孟生旺.负二项回归模型的推广及其在分类费率厘定中的应用[J].数理统计与管理,2010,29(4):656-661.
    [88]徐昕,袁卫,孟生旺.零膨胀负二项回归模型的推广与费率厘定[J].系统工程理论与实践,2012,32(1):127-133.
    [89]项丽雅,朱仲义.两种ZIP模型的比较及其在保费厘定中的应用[J].数理统计与管理,2013,32(5):854-862.
    [90]孙维伟,张连增.ZAIG模型在车险定价中的应用研究[J].保险研究,2013,(4):43-51.
    [91]孟生旺,王选鹤.GAMLSS模型及其在车损险费率厘定中的应用[J].数理统计与管理,2014,33(4):583-591.
    [92]Smyth G K.Generalized linear models with varying dispersion[J].Journal of the Royal Statistical Society(Series B),1989,51(1):47-60.
    [93]Verbeke G,Molenberghs G.Linear Mixed Models for Longitudinal Data[M].Berlin:Springer-Verlag,2000.
    [94]Goldstein H.Multilevel Statistical Models(2nd ed.)[M].New York:John Wiley,1995.
    [95]Longford N.Random Coefficient Models[M].Oxford:Oxford University Press,1993.
    [96]Nelder J A,Lee Y.Generalized linear models for the analysis of taguchi-type experiments[J].Applied Stochastic Models and Data Analysis,1991,7(1):107-120.
    [97]Zeger S L,Diggle P J.Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters[J].Biometrics,1994,50:689-699.
    [98]Sun J,Frees E W,Rosenberg M A.Heavy-tailed longitudinal data modeling using copulas[J].Insurance:Mathematics and Economics,2008,42(2):817-830.
    [99]Frees E W.Regression Modeling with Actuarial and Financial Application[M].New York:Cambridge University Press,2010.
    [100]Czado C,Kastenmeier R,Brechmann E C,et al.A mixed copula model for insurance claims and claim sizes[J].Scandinavian Actuarial Journal,2012,2012(4):278-305.
    [101]孟生旺,刘新红.基于copula回归模型的损失预测[J].统计与信息论坛,2013,28(9):27-31.
    [102]Zhao X,Zhou X.Copula-based dependence between frequency and class in car insurance with excess zeros[J].Operations Research Letters,2014,42(4):273-277.
    [103]Shi P,Valdez E A.Multivariate negative binomial models for insurance claim counts[J].Insurance:Mathematics and Economics,2014,55(1):18-29.
    [104]Shi P.Insurance ratemaking using a copula-based multivariate Tweedie model[J].Scandinavian Actuarial Journal,2016,2016(3):198-215.
    [105]Wen L,Wu X,Zhou X.The credibility premiums for models with dependence induced by common effects[J].Insurance:Mathematics and Economics,2009,44(1):19-25.
    [106]Frees E W,Wang P.Copula credibility for aggregate loss models[J].Insurance:Mathematics and Economics,2006,38(2):360-373.
    [107]Yeo K L,Valdez E A.Claim dependence with common effects in credibility models[J].Insurance:Mathematics and Economics,2006,38(3):609-629.
    [108]张连增,段白鸽.准备金评估的随机性Munich链梯法及改进—基于Bootstrap方法的实证分析[J].数量经济技术经济研究,2011,28(11):98-111.
    [109]张连增,段白鸽.基于已决赔款与己报案赔款相关性的随机性准备金进展法[J].管理评论,2013,25(5):11-22.
    [110]孟生旺,袁卫.大数据时代的统计教育[J].统计研究,2015,32(4):3-7.

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