再保险决策中的数据包络分析
|
摘要
保险业是经营风险的特殊金融服务行业。随着社会经济的发展和现代科学技
术的广泛应用,一次事故可能造成的物质损失和人身伤亡的损失程度不断扩大,任
何保险公司也不敢独自承担巨额的风险，保险监管部门也不允许这样做。为保持
经营的稳定性，扩大业务规模，再保险成为必然的选择。再保险种基本问题是自
留额的选择，即原保险人自留多少？分保多少的问题？理论上对自留额的确定利
用效应函数来解决，然而效应函数是一种主观、因人而异并难以确定的。因此把
效应方法用于实际再保险决策问题是难以操作的。
DEA 方法是评价具有相同类型投入和产出的若干生产与非生产部门 (简称
决策单元) 相对效率的系统分析方法.广泛用于来评价生产活动的最优性.然而在
现实的经济活动中,投入产出因素往往受到随机因素的干扰,由此而产生测量误差,
数据噪声.同时经济现象本身也具有波动性及周期性,因此.决策单元的输入和输
出往往不是确定的数值,而是服从一定随机分布的变量,因而应用确定性的 DEA
模型[1]求解，具有较大的局限性.
本文在广泛查阅国内外文的基础上，对 DEA 理论、方法与应用进行了较深
入地探讨，分析了基本的 DEA 模型，DEA 有效性理论以及 DEA 方法的基本思
想，基于分治思想对随机 DMU 有效性的进行了分析，提出了一种新的随机 DMU
问题的求解方法,主要讨论了输入输出均具有共同趋向的多输入多输出的随机
DEA 问题的求解过程和算法。基于均值-方差原理讨论了随机 DMU 的相对稳定
有效性。结合再保险的理论，将数据包络思想应用到再保险决策中，对再保险中
再保险方案的选择、预测再保险的有效性进行了分析，具有较强的实用性。
Insurance is a special finance trade of managing risk. As the development of
society and economy, technology and science are applied abroad, the degree of loss of
matter and casualty enlarged in an accident. Any insurance dare not bear the risk of
mint and it is not allowed by wardship. To keep stability and enlarge the scale of
managing, reinsurance becomes the necessity choice, the basic problem of reinsurance
is to deal with premium and keep retention. In theory, it can be answered by utility.
but utility function is subjective and can’t define easily, so to apply the means of
utility in practice of decision-making of reinsurance is difficulty.
Data envelopment analysis (DEA) is a power technique of measuring the relative
efficiency of a set of decision-making units (DMUs) with the same inputs and outputs.
This technique has been widely applied in measuring the optimal property, but in the
activity of economy, inputs and outputs is disturbed by error and fluctuate and
periodicity, so the stochastic data variations in inputs and outputs may be incorporated
into the DEA framework for evaluating the efficiency.
In this paper, the development of Data Envelopment Analysis (DEA) theories,
DEA methods and DEA applications are discussed, the basic DEA model DEA
efficiency theories are analyzed. Based on divided and conquer, the define of
evaluation of stochastic DMU from another aspect is presented and given a new
method of solving, the process and algorithm of many input and output stochastic
DMU provided with common trend is discussed in main. Based on principle of
mean-variance, this paper firstly advances this definition of the relative -stable
efficiency of stochastic DMUS and presents the model DEA of the relative-stable
efficiency measurement and analyses the relative-stable efficiency, and gives the
calculation of it. The idea of data envelopment analysis is applied into
decision-making of reinsurance, implying the choice project and the forecasting the
relative efficiency of reinsurance and analyzing the feasibility of algorithm.
术的广泛应用,一次事故可能造成的物质损失和人身伤亡的损失程度不断扩大,任
何保险公司也不敢独自承担巨额的风险，保险监管部门也不允许这样做。为保持
经营的稳定性，扩大业务规模，再保险成为必然的选择。再保险种基本问题是自
留额的选择，即原保险人自留多少？分保多少的问题？理论上对自留额的确定利
用效应函数来解决，然而效应函数是一种主观、因人而异并难以确定的。因此把
效应方法用于实际再保险决策问题是难以操作的。
DEA 方法是评价具有相同类型投入和产出的若干生产与非生产部门 (简称
决策单元) 相对效率的系统分析方法.广泛用于来评价生产活动的最优性.然而在
现实的经济活动中,投入产出因素往往受到随机因素的干扰,由此而产生测量误差,
数据噪声.同时经济现象本身也具有波动性及周期性,因此.决策单元的输入和输
出往往不是确定的数值,而是服从一定随机分布的变量,因而应用确定性的 DEA
模型[1]求解，具有较大的局限性.
本文在广泛查阅国内外文的基础上，对 DEA 理论、方法与应用进行了较深
入地探讨，分析了基本的 DEA 模型，DEA 有效性理论以及 DEA 方法的基本思
想，基于分治思想对随机 DMU 有效性的进行了分析，提出了一种新的随机 DMU
问题的求解方法,主要讨论了输入输出均具有共同趋向的多输入多输出的随机
DEA 问题的求解过程和算法。基于均值-方差原理讨论了随机 DMU 的相对稳定
有效性。结合再保险的理论，将数据包络思想应用到再保险决策中，对再保险中
再保险方案的选择、预测再保险的有效性进行了分析，具有较强的实用性。
Insurance is a special finance trade of managing risk. As the development of
society and economy, technology and science are applied abroad, the degree of loss of
matter and casualty enlarged in an accident. Any insurance dare not bear the risk of
mint and it is not allowed by wardship. To keep stability and enlarge the scale of
managing, reinsurance becomes the necessity choice, the basic problem of reinsurance
is to deal with premium and keep retention. In theory, it can be answered by utility.
but utility function is subjective and can’t define easily, so to apply the means of
utility in practice of decision-making of reinsurance is difficulty.
Data envelopment analysis (DEA) is a power technique of measuring the relative
efficiency of a set of decision-making units (DMUs) with the same inputs and outputs.
This technique has been widely applied in measuring the optimal property, but in the
activity of economy, inputs and outputs is disturbed by error and fluctuate and
periodicity, so the stochastic data variations in inputs and outputs may be incorporated
into the DEA framework for evaluating the efficiency.
In this paper, the development of Data Envelopment Analysis (DEA) theories,
DEA methods and DEA applications are discussed, the basic DEA model DEA
efficiency theories are analyzed. Based on divided and conquer, the define of
evaluation of stochastic DMU from another aspect is presented and given a new
method of solving, the process and algorithm of many input and output stochastic
DMU provided with common trend is discussed in main. Based on principle of
mean-variance, this paper firstly advances this definition of the relative -stable
efficiency of stochastic DMUS and presents the model DEA of the relative-stable
efficiency measurement and analyses the relative-stable efficiency, and gives the
calculation of it. The idea of data envelopment analysis is applied into
decision-making of reinsurance, implying the choice project and the forecasting the
relative efficiency of reinsurance and analyzing the feasibility of algorithm.
引文
参考文献
[1]谢志刚,韩天雄.风险理论与非寿险精算.天津:南开大学出版社 2000.6
[2]Charnes A.Cooper W.W and E,Rhodes:Measring the efficiency of decision making
units,Europment Journal of Operational Research,1978,2:429-444.
[3]Seiford L M.Data Envelopment Analysis: the evolution of state of
art(1978-1995).Journal of Production Analysis,1996,7:99-137.
[4]魏权龄.评价相对有效性的 DEA 方法.北京;中国人民大学出版社,1988.
[5]盛昭瀚,朱乔,吴广谋. DEA 理论方法与应用[M] 北京:科学出版社,1996
[6]Charnes A.Cooper W.W.etal.Data envelopment analysis:Theory,methodology and
application.USA:Kluwwer Academic publishers,Boston,1994.
[7]Charnes A.Cooper W.W et al,Foundation of data envelopment analysis for
Pareto-Koomans efficient empirical production function .J.of
Econometris,1985,30(1/2):91-107.
[8]保罗,A.萨缪尔森,威廉 D.偌德豪斯著.胡代光等译.经济学(第十四版).北京:首都
经济贸易大学出版社,1996.
[9]Charnes A.Cooper W.W et al,Invariant multiplicative for efficiency and price wise
codd-douglas envelopment.Operations research letters,1983,2(3):101-103.
[10]Rolf Fare,Shawana Grosskopf et al.The Measurement of Efficiency of
Production .Kkuwer-Nijhoff Publishing.
[11]李果,王英明,总体有效的 DEA 模型.预测,1999,（3）:54-55.
[12]李光金,刘永清.基于多目标规划的 DEA.系统工程理论与实践,1997,（3）:16-22.
[13]谢艾国等.全局 DEA 模型研究.系统工程与电子技术,1999,24（5）:1-5.
[14]黄弢,李光金等.综合 DEA 模型的理论研究[J].系统工程理论方法应用
2000.9(4).
[15]魏权龄.数据包络分析(DEA).科学通报,2000,45(17),1793-1808
[16]Charnes A.Cooper W.W.Wei Q L.et al.Cone ratio Data Envelopment Analysis and
multi-objective programming. international Journal of Science,1989.20(7):1099-1118
41
参考文献
[17]Yu G, Wei Q L, Brockett P. A generalized Data Envelopment Analysis
model.Annals of Operation Research.1996,66:47-89.
[18]Charnes A.Cooper W.W.Wei Q L.et al.Compositive Data Envelopment Analysis
and Multiobjective Programming.Center for Cybernetic Studies Report CCS 633,1988
[19]Sengupta J K. Data envelopment analysis fou efficiency measurement in the stochastic
case[J].Comput.Oper. Res.1987,14:117-129
[20]Land K C. Lovell C A K.Thore S. Chance-constrained Data Envelopment Analysis.
Managerial and Decision Economics.1993,14:541-554.
[21]Huang Z M, Li S X. Dominance Stochastic Models in Data Envelopment
Analysis[J].European Journal of Operational Research,1996,95:370-403.
[22]Banker R D. Maximum Likelihood, Consistency and DEA Statistical
Foundation[J], Management Science,1993,39:11265-1273
[23]肖渡等.数据包络分析与极大似然估计[J].系统工程理论方法与应用.1996,16
（1）:45-50 .
[24]Olesen O B, Petersen N C. Chance Constrained Efficiency Evaluation[J].
Management Science, 1995,41:442-457.
[25] [20] Sengupta J K. Transformation in stochastic DEA models[J]. J.
Econometrics,1990,46:109-123
Cooper W W, Huang Z M, et al. Satisfying DEA Models Under Chance
Constraints[J]. Annals of Operation Research,1996,66:279-295.
[26] 胡汉辉等 . 数据包络模型的随机型研究 [J]. 系统工程学报 . 1995,10
(4):101-107.
[27]官建成，王军霞. DEA 灵敏度分析的进一步探讨与应用[J]. 系统工程理论与
实践.2003,1:37-43.
[28]李光金 评价相对效率的投入-产出型 DEA. 管理科学学报 2000.4(2)
[29]吴文江 两个新的数据包络分析(DEA)模型的探讨 系统工程理论方法应用
2001.10(3).
[1]谢志刚,韩天雄.风险理论与非寿险精算.天津:南开大学出版社 2000.6
[2]Charnes A.Cooper W.W and E,Rhodes:Measring the efficiency of decision making
units,Europment Journal of Operational Research,1978,2:429-444.
[3]Seiford L M.Data Envelopment Analysis: the evolution of state of
art(1978-1995).Journal of Production Analysis,1996,7:99-137.
[4]魏权龄.评价相对有效性的 DEA 方法.北京;中国人民大学出版社,1988.
[5]盛昭瀚,朱乔,吴广谋. DEA 理论方法与应用[M] 北京:科学出版社,1996
[6]Charnes A.Cooper W.W.etal.Data envelopment analysis:Theory,methodology and
application.USA:Kluwwer Academic publishers,Boston,1994.
[7]Charnes A.Cooper W.W et al,Foundation of data envelopment analysis for
Pareto-Koomans efficient empirical production function .J.of
Econometris,1985,30(1/2):91-107.
[8]保罗,A.萨缪尔森,威廉 D.偌德豪斯著.胡代光等译.经济学(第十四版).北京:首都
经济贸易大学出版社,1996.
[9]Charnes A.Cooper W.W et al,Invariant multiplicative for efficiency and price wise
codd-douglas envelopment.Operations research letters,1983,2(3):101-103.
[10]Rolf Fare,Shawana Grosskopf et al.The Measurement of Efficiency of
Production .Kkuwer-Nijhoff Publishing.
[11]李果,王英明,总体有效的 DEA 模型.预测,1999,（3）:54-55.
[12]李光金,刘永清.基于多目标规划的 DEA.系统工程理论与实践,1997,（3）:16-22.
[13]谢艾国等.全局 DEA 模型研究.系统工程与电子技术,1999,24（5）:1-5.
[14]黄弢,李光金等.综合 DEA 模型的理论研究[J].系统工程理论方法应用
2000.9(4).
[15]魏权龄.数据包络分析(DEA).科学通报,2000,45(17),1793-1808
[16]Charnes A.Cooper W.W.Wei Q L.et al.Cone ratio Data Envelopment Analysis and
multi-objective programming. international Journal of Science,1989.20(7):1099-1118
41
参考文献
[17]Yu G, Wei Q L, Brockett P. A generalized Data Envelopment Analysis
model.Annals of Operation Research.1996,66:47-89.
[18]Charnes A.Cooper W.W.Wei Q L.et al.Compositive Data Envelopment Analysis
and Multiobjective Programming.Center for Cybernetic Studies Report CCS 633,1988
[19]Sengupta J K. Data envelopment analysis fou efficiency measurement in the stochastic
case[J].Comput.Oper. Res.1987,14:117-129
[20]Land K C. Lovell C A K.Thore S. Chance-constrained Data Envelopment Analysis.
Managerial and Decision Economics.1993,14:541-554.
[21]Huang Z M, Li S X. Dominance Stochastic Models in Data Envelopment
Analysis[J].European Journal of Operational Research,1996,95:370-403.
[22]Banker R D. Maximum Likelihood, Consistency and DEA Statistical
Foundation[J], Management Science,1993,39:11265-1273
[23]肖渡等.数据包络分析与极大似然估计[J].系统工程理论方法与应用.1996,16
（1）:45-50 .
[24]Olesen O B, Petersen N C. Chance Constrained Efficiency Evaluation[J].
Management Science, 1995,41:442-457.
[25] [20] Sengupta J K. Transformation in stochastic DEA models[J]. J.
Econometrics,1990,46:109-123
Cooper W W, Huang Z M, et al. Satisfying DEA Models Under Chance
Constraints[J]. Annals of Operation Research,1996,66:279-295.
[26] 胡汉辉等 . 数据包络模型的随机型研究 [J]. 系统工程学报 . 1995,10
(4):101-107.
[27]官建成，王军霞. DEA 灵敏度分析的进一步探讨与应用[J]. 系统工程理论与
实践.2003,1:37-43.
[28]李光金 评价相对效率的投入-产出型 DEA. 管理科学学报 2000.4(2)
[29]吴文江 两个新的数据包络分析(DEA)模型的探讨 系统工程理论方法应用
2001.10(3).