判别分析在机动车辆保险费率厘定中的应用
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摘要
随着我国保险体制改革的逐渐深化以及国外保险公司的全面进入,我国保险业的竞争日趋激烈。谁能够正确的分析隐藏在保险公司客户数据中的信息,谁就能更好地控制理赔风险,提供更好的保险产品与服务,从而在激烈的竞争中获胜。
判别分析是多元统计分析中应用广泛的统计方法,是根据表明事物特点的变量值和它们所属的类,求出判别函数,根据判别函数对未知所属类别的事物进行分类的一种分析方法。在判别分析方法中经常使用的有Fisher判别和Bayes判别。Fisher判别是依据方差分析原理建立起来的一种判别分析方法,Fisher判别的基本思路就是投影使得变换后的数据中同类别的点“尽可能聚在一起”,不同类别的点“尽可能分离”,以此达到分类的目的。Bayes判别是一种概率型的判别分析方法,在分析过程开始时需要获得各个类别的分布密度函数,同时也需要知道样本点属于各个类别的先验概率,总结出客观事物分类的规律性建立判别函数,而分析过程结束时则计算每个样本点归属于某个类别的最大概率或最小错判损失,以确定各个样本点的预测类别归属。判别分析已经应用于许多领域中,如:在地质勘探中,根据岩石标本判别地质年代;在经济研究中,通过多个指标来判定一个国家的经济发展水平;在公司财务分析中,根据上市公司的财务指标,对其财务健康状况给予分析和评价,对即将到来的财务危机做出预警;在市场预测中,根据以往的调查数据判别下一季度产品的适销情况等。
论文将判别分析方法引入到机动车辆保险费率厘定中,重点研究如何运用判别分析方法来提高机动车险费率厘定的准确性。论文运用Fisher判别分析法和Bayes判别分析法对保险公司的数据进行了实证研究,并结合实际经验与保险学理论对这两种判别分析方法的判别效果进行了比较。研究结果表明,将判别分析应用到机动车辆保险费率厘定中是可行的。判别分析可以用来检验保险公司的分类是否准确、收取的费率是否恰当。在考虑了诸风险因素的情况下,应用判别分析可以更加充分地挖掘可用信息,降低错判率,使得费率厘定更加准确。
With the development of China's insurance system’s reform and the comprehensive entry of foreign insurance companies, our own insurance industry has to face the fierce competition increasingly. Those who can analyze the information that hide in the insurance companies’customers data correctly, will be able to control the claims risk better, and can also provide customers with better insurance products and services. Finally, they will win in the fierce competition.
Discriminant analysis is a statistical method that can be widely applied in the multivariate statistical analysis, and it is based on the variables’value of characteristics of things and their own class to get the discriminant function. It is a kind of analysis method that we make classification on unknown things based on discriminant function. There are Fisher discriminant and Bayes discriminant in Discriminant analysis methods, which are often used. Bayes discriminant is a discriminant analysis which is based on probability. In the beginning of analysis we need get distribution density function of every class, and also need to know the prior probability that various types of sample points belong to every class. At the same time, we sum up the regularity of objective things classification to establish discriminant function; at the end of the analysis, we calculate the largest probability and the smallest misjudgement loss that each sample point belongs to some class and determine which predicting class every sample point belongs to.Fisher discriminant is another method of discriminant analysis, based on the principle of analysis of variance. The basic idea of Fisher discriminant is to project and make the same types of points of transformed data points "as near as possible", and different types of points "as far as possible separation" to achieve the purpose of classification. Discriminant analysis has been applied in many fields, such as: in companies' financial analysis, to give analysis and evaluation of the financial health status and make early warning of upcoming financial crisis, based on the financial indicators of listed companies; in the market prediction, to determine whether or not the products is ready sell in the next quarter based on previous survey data.
We apply discriminant analysis to the system of rate of automobile premium, and focus on how to improve the accuracy of rate-making of vehicles risk in the application of discriminant analysis. We use Fisher and Bayes discriminant analysis methods respectively to do empirical study on insurance data, and do some comparison job between discriminant results of the two discriminant analysis methods, combined with of practical experience and the insurance theory. The study illustrates it is feasible in theory to do the discriminant analysis in the rate redefinition of automobile premium. Discriminant analysis can test whether the classification of insurance companies is accurate and rates are reasonably charged. After taking into account the various risk factors, the application of discriminant analysis can more fundamentally mine the available information, which will lower the probability of erroneous judgment and make rate redefinition of automobile premium more accurate.
判别分析是多元统计分析中应用广泛的统计方法,是根据表明事物特点的变量值和它们所属的类,求出判别函数,根据判别函数对未知所属类别的事物进行分类的一种分析方法。在判别分析方法中经常使用的有Fisher判别和Bayes判别。Fisher判别是依据方差分析原理建立起来的一种判别分析方法,Fisher判别的基本思路就是投影使得变换后的数据中同类别的点“尽可能聚在一起”,不同类别的点“尽可能分离”,以此达到分类的目的。Bayes判别是一种概率型的判别分析方法,在分析过程开始时需要获得各个类别的分布密度函数,同时也需要知道样本点属于各个类别的先验概率,总结出客观事物分类的规律性建立判别函数,而分析过程结束时则计算每个样本点归属于某个类别的最大概率或最小错判损失,以确定各个样本点的预测类别归属。判别分析已经应用于许多领域中,如:在地质勘探中,根据岩石标本判别地质年代;在经济研究中,通过多个指标来判定一个国家的经济发展水平;在公司财务分析中,根据上市公司的财务指标,对其财务健康状况给予分析和评价,对即将到来的财务危机做出预警;在市场预测中,根据以往的调查数据判别下一季度产品的适销情况等。
论文将判别分析方法引入到机动车辆保险费率厘定中,重点研究如何运用判别分析方法来提高机动车险费率厘定的准确性。论文运用Fisher判别分析法和Bayes判别分析法对保险公司的数据进行了实证研究,并结合实际经验与保险学理论对这两种判别分析方法的判别效果进行了比较。研究结果表明,将判别分析应用到机动车辆保险费率厘定中是可行的。判别分析可以用来检验保险公司的分类是否准确、收取的费率是否恰当。在考虑了诸风险因素的情况下,应用判别分析可以更加充分地挖掘可用信息,降低错判率,使得费率厘定更加准确。
With the development of China's insurance system’s reform and the comprehensive entry of foreign insurance companies, our own insurance industry has to face the fierce competition increasingly. Those who can analyze the information that hide in the insurance companies’customers data correctly, will be able to control the claims risk better, and can also provide customers with better insurance products and services. Finally, they will win in the fierce competition.
Discriminant analysis is a statistical method that can be widely applied in the multivariate statistical analysis, and it is based on the variables’value of characteristics of things and their own class to get the discriminant function. It is a kind of analysis method that we make classification on unknown things based on discriminant function. There are Fisher discriminant and Bayes discriminant in Discriminant analysis methods, which are often used. Bayes discriminant is a discriminant analysis which is based on probability. In the beginning of analysis we need get distribution density function of every class, and also need to know the prior probability that various types of sample points belong to every class. At the same time, we sum up the regularity of objective things classification to establish discriminant function; at the end of the analysis, we calculate the largest probability and the smallest misjudgement loss that each sample point belongs to some class and determine which predicting class every sample point belongs to.Fisher discriminant is another method of discriminant analysis, based on the principle of analysis of variance. The basic idea of Fisher discriminant is to project and make the same types of points of transformed data points "as near as possible", and different types of points "as far as possible separation" to achieve the purpose of classification. Discriminant analysis has been applied in many fields, such as: in companies' financial analysis, to give analysis and evaluation of the financial health status and make early warning of upcoming financial crisis, based on the financial indicators of listed companies; in the market prediction, to determine whether or not the products is ready sell in the next quarter based on previous survey data.
We apply discriminant analysis to the system of rate of automobile premium, and focus on how to improve the accuracy of rate-making of vehicles risk in the application of discriminant analysis. We use Fisher and Bayes discriminant analysis methods respectively to do empirical study on insurance data, and do some comparison job between discriminant results of the two discriminant analysis methods, combined with of practical experience and the insurance theory. The study illustrates it is feasible in theory to do the discriminant analysis in the rate redefinition of automobile premium. Discriminant analysis can test whether the classification of insurance companies is accurate and rates are reasonably charged. After taking into account the various risk factors, the application of discriminant analysis can more fundamentally mine the available information, which will lower the probability of erroneous judgment and make rate redefinition of automobile premium more accurate.
引文
1文东.机动车辆保险费率市场化研究—以永安保险公司机动车辆保险费率厘定为例[D] .重庆:重庆大学,2003年
2 2008-2012年中国汽车保险行业市场发展及前景展望分析报告.http://www.hdcmr.com/article/yjbg/13/02/22051.html:2008年07月22日
3田冲.数据挖掘技术在我国汽车保险业中的应用研究[D].武汉:武汉理工大学,2007年
4张俊岭,张俊峰.非寿险费率厘定中的分类费率因子研究[J].保险研究,2008年第1期:77页
[1]蔡建琼,于慧芳,朱志洪等.SPSS统计分析实例精选[M].北京:清华大学出版社,2006年:308-334.
[2]吴喜之.统计学:从数据到结论[M].北京:中国统计出版社,2006年:190-198.
[3]于秀林,任雪松.多元统计分析[M].北京:中国统计出版社,1999年:128-151.
[4]王灵犀,王伟.机动车辆保险与理赔实务[M].北京:人民交通出社,2004年:74-90.
[5]王保进.多变量分析——统计软件与数据分析[M].北京:北京大学出版社,2007年:113-128.
[6]杜先凯.汽车保险的费率厘定研究[J].上海保险,2003第8期:33-35.
[7]韩明莲,卢书成,张袆.Fisher多类判别分析法在期货价格预测中的应用[J].统计应用,2007年第5期:43-44.
[8]韩天雄,夏荣良.费率市场化的精算技术准备[J].上海保险,2003年第5期:27-28.
[9]晋波.汪健兵精算在机动车辆保险中的应用[J].上海保险,2000年第9期:29-31.
[10]雷兢,沈斐敏.贝叶斯(Bayes)判别分析理论在安全评价中的应用[J].工业安全与环保,2004年第5期:39-40.
[11]李斌.房地产估价的贝叶斯判别法[J].武汉城市建设学院学报,1993年第3-4期:27-33.
[12]李映,焦李成.基于核Fisher判别分析的目标识别[J].西安电子科技大学学报(自然科学版),2003年第4期:179-182.
[13]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年第4期:26-29.
[14]毛泽春,刘锦尊.广义线性模型与保费点数计价系统[J].统计研究,2002第6期:23-25.
[15]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,2006年第4期:584-588.
[16]瞿玲.对财产保险公司监管指标的实证分析[J].精算通讯,2002年第3卷第3期:43-46.
[17]沈明刚.试论实施机动车辆保险风险等级费率之必要[J].保险研究,2001年第6期:25-26.
[18]孙佳美.对我国机动车辆保险费率厘定因素的思考[J].保险研究,2004年第11期:34-37.
[19]谢菁莲.中国机动车辆保险费率厘定的研究浅析[J].当代经理人,2006第5期:60-61.
[20]徐少锋.Fisher判别分析在个人信用评估中的应用[J].统计与决策,2006年第3期:133-135.
[21]曾辉,范兴华.关于我国机动车辆保险费率厘定因素的思考[J].经济师,2003年第2期:22-26.
[22]曾理斌.广义线性模型在非寿险费率厘定中的运用[J].金融经济,2007年第18期:60-61.
[23]张俊岭,张俊峰.非寿险费率厘定中的分类费率因子研究[J].保险研究,2008年第1期:77-81
[24]王慧萍.我国机动车辆保险分类费率厘定的实证研究[D].湖南:湖南大学,2005年:1-13.
[25]陈军.火山碎屑岩岩性的测井识别方法研究[D].吉林:吉林大学,2008年:1-4.
[26]田冲.数据挖掘技术在我国汽车保险业中的应用研究[D].武汉:武汉理工大学,2007年:6-8.
[27]文东.机动车辆保险费率市场化研究—以永安保险公司机动车辆保险费率厘定为例[D] .重庆:重庆大学,2003年:6.
[28]谢亚鹏.判别分析在上市公司信用风险度量中的应用[D].吉林:吉林大学,2004年:1-3.
[29]张茵.对加入从人因素的我国车辆费率厘定的研究[D].湖南:湖南大学,2007年:8-26.
[30] 2008-2012年中国汽车保险行业市场发展及前景展望分析报告[EB/OL].http://www.hdcmr.com/article/yjbg/13/02/22051.html:2008年07月22日
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2 2008-2012年中国汽车保险行业市场发展及前景展望分析报告.http://www.hdcmr.com/article/yjbg/13/02/22051.html:2008年07月22日
3田冲.数据挖掘技术在我国汽车保险业中的应用研究[D].武汉:武汉理工大学,2007年
4张俊岭,张俊峰.非寿险费率厘定中的分类费率因子研究[J].保险研究,2008年第1期:77页
[1]蔡建琼,于慧芳,朱志洪等.SPSS统计分析实例精选[M].北京:清华大学出版社,2006年:308-334.
[2]吴喜之.统计学:从数据到结论[M].北京:中国统计出版社,2006年:190-198.
[3]于秀林,任雪松.多元统计分析[M].北京:中国统计出版社,1999年:128-151.
[4]王灵犀,王伟.机动车辆保险与理赔实务[M].北京:人民交通出社,2004年:74-90.
[5]王保进.多变量分析——统计软件与数据分析[M].北京:北京大学出版社,2007年:113-128.
[6]杜先凯.汽车保险的费率厘定研究[J].上海保险,2003第8期:33-35.
[7]韩明莲,卢书成,张袆.Fisher多类判别分析法在期货价格预测中的应用[J].统计应用,2007年第5期:43-44.
[8]韩天雄,夏荣良.费率市场化的精算技术准备[J].上海保险,2003年第5期:27-28.
[9]晋波.汪健兵精算在机动车辆保险中的应用[J].上海保险,2000年第9期:29-31.
[10]雷兢,沈斐敏.贝叶斯(Bayes)判别分析理论在安全评价中的应用[J].工业安全与环保,2004年第5期:39-40.
[11]李斌.房地产估价的贝叶斯判别法[J].武汉城市建设学院学报,1993年第3-4期:27-33.
[12]李映,焦李成.基于核Fisher判别分析的目标识别[J].西安电子科技大学学报(自然科学版),2003年第4期:179-182.
[13]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年第4期:26-29.
[14]毛泽春,刘锦尊.广义线性模型与保费点数计价系统[J].统计研究,2002第6期:23-25.
[15]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,2006年第4期:584-588.
[16]瞿玲.对财产保险公司监管指标的实证分析[J].精算通讯,2002年第3卷第3期:43-46.
[17]沈明刚.试论实施机动车辆保险风险等级费率之必要[J].保险研究,2001年第6期:25-26.
[18]孙佳美.对我国机动车辆保险费率厘定因素的思考[J].保险研究,2004年第11期:34-37.
[19]谢菁莲.中国机动车辆保险费率厘定的研究浅析[J].当代经理人,2006第5期:60-61.
[20]徐少锋.Fisher判别分析在个人信用评估中的应用[J].统计与决策,2006年第3期:133-135.
[21]曾辉,范兴华.关于我国机动车辆保险费率厘定因素的思考[J].经济师,2003年第2期:22-26.
[22]曾理斌.广义线性模型在非寿险费率厘定中的运用[J].金融经济,2007年第18期:60-61.
[23]张俊岭,张俊峰.非寿险费率厘定中的分类费率因子研究[J].保险研究,2008年第1期:77-81
[24]王慧萍.我国机动车辆保险分类费率厘定的实证研究[D].湖南:湖南大学,2005年:1-13.
[25]陈军.火山碎屑岩岩性的测井识别方法研究[D].吉林:吉林大学,2008年:1-4.
[26]田冲.数据挖掘技术在我国汽车保险业中的应用研究[D].武汉:武汉理工大学,2007年:6-8.
[27]文东.机动车辆保险费率市场化研究—以永安保险公司机动车辆保险费率厘定为例[D] .重庆:重庆大学,2003年:6.
[28]谢亚鹏.判别分析在上市公司信用风险度量中的应用[D].吉林:吉林大学,2004年:1-3.
[29]张茵.对加入从人因素的我国车辆费率厘定的研究[D].湖南:湖南大学,2007年:8-26.
[30] 2008-2012年中国汽车保险行业市场发展及前景展望分析报告[EB/OL].http://www.hdcmr.com/article/yjbg/13/02/22051.html:2008年07月22日
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