非负约束权重的个人信用评估组合预测模型研究
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摘要
随着我国消费信贷市场的不断发展,个人信用得到了空前的重视。我国目前尚未建立起完善的个人征信体系,商业银行目前没有一套科学合理的个人信用评估指标和方法。在这种情况下,加强对个人信用评估方法的研究,对于商业银行降低消费信贷风险,减少不良贷款比率,扩大消费信贷的积极性,促进国民经济快速稳定发展具有积极意义。
本文在对国内外相关研究成果进行分析的基础上,首先阐述了个人信用评估中用到的三种统计方法的基本原理并分别建立了基于这三种统计方法的个人信用评估模型并进行了检验,随后对组合预测原理及其权重求解的方法进行了阐述,最后构建了基于线性回归、Logistic回归和Probit回归三种统计方法的非负约束权重的组合预测模型,并将组合预测模型应用到个人信用评估中。在非负约束权重的组合预测模型的权重求解计算中,引入了较传统解法更有效、结果更合理的二次规划的神经网络解法,并且利用遗传算法对非负权重进行了求解。在最后的模型应用中,将非负约束权重的组合预测模型与单一模型进行对比,结果表明:从总分类准确率和总错分率来看,三种单一统计模型及组合预测模型的分类准确率都在90%以上,其中非负约束权重的组合预测模型的总分类效果最好,与此同时非负约束权重的组合预测模型的第一类错分率虽然不是最低,但在第二类错分率上具有优势,因此可以判定非负约束权重的组合预测模型的分类综合效果高于单一模型。将利用二次规划算法求解的非负约束权重的组合预测模型与利用遗传算法求解得到的非负约束权重的组合预测模型进行对比表明,二次规划算法中线性回归模型的权重为0,作为冗余方法被剔除,并且前者的分类效果优于利用遗传算法求解得到的结果。由此得出,利用二次规划方法求解得到的非负约束权重的组合预测模型在个人信用评估中是具有应用价值的结论。
With the development of consumer credit in domestic commercial banks, personal credit becomes more and more important. At present there is no perfect personal credit system established in China, and there are no scientific and reasonable methods or indicators applied in personal credit assessment. In this situation, researches on personal credit scoring are critical for the commercial banks to reduce the risk of personal credit and the ratio of non-performing loan. It also has a positive significance for the commercial banks to expand the consumer credit market which can accelerate and stabilize the development of the national economy.
Based on analysis of domestic and overseas in personal credit scoring, this dissertation firstly expatiates on the fundamental principles of the three statistical methods to be used in this domain and then establishes and tests the three models in personal credit scoring respectively. Then it elaborates the principles of combining forecasts as well as its methods of weights calculation. At last, after establishing a combined forecast model with non-negative combining weight constraint through multi-linear regression, logistic regression and Probit regression, this dissertation applies the combined model to personal credit scoring. In the weights calculation of the combination forecasting model, the dissertation uses the method Genetic Algorithms and introduces a new Neural Networks method of quadratic programming, which is more effective and reasonable. Through the contrast of the combining model with non-positive restriction on weights and the single ones in the final application, the result shows that the general accuracy of the models are all above 90%, while the effect of the combination forecasting model is better. At the same time, in the result of the combination forecasting model, the error rate of the first case is not the lowest, but its error rate of the second case has a comparative advantage. Therefore the combination forecasting model with non-negative combining weight constraint is generally better than the single ones. Through the contrast between the results of the two methods it shows that the weight of Multiple Linear Regression in quadratic programming is 0, so it is rejected. And the effect of classification based on the method of quadratic programming is better. Therefore it can be concluded that the combination forecasting model using Neural Networks of quadratic programming has an application value in personal credit scoring.
本文在对国内外相关研究成果进行分析的基础上,首先阐述了个人信用评估中用到的三种统计方法的基本原理并分别建立了基于这三种统计方法的个人信用评估模型并进行了检验,随后对组合预测原理及其权重求解的方法进行了阐述,最后构建了基于线性回归、Logistic回归和Probit回归三种统计方法的非负约束权重的组合预测模型,并将组合预测模型应用到个人信用评估中。在非负约束权重的组合预测模型的权重求解计算中,引入了较传统解法更有效、结果更合理的二次规划的神经网络解法,并且利用遗传算法对非负权重进行了求解。在最后的模型应用中,将非负约束权重的组合预测模型与单一模型进行对比,结果表明:从总分类准确率和总错分率来看,三种单一统计模型及组合预测模型的分类准确率都在90%以上,其中非负约束权重的组合预测模型的总分类效果最好,与此同时非负约束权重的组合预测模型的第一类错分率虽然不是最低,但在第二类错分率上具有优势,因此可以判定非负约束权重的组合预测模型的分类综合效果高于单一模型。将利用二次规划算法求解的非负约束权重的组合预测模型与利用遗传算法求解得到的非负约束权重的组合预测模型进行对比表明,二次规划算法中线性回归模型的权重为0,作为冗余方法被剔除,并且前者的分类效果优于利用遗传算法求解得到的结果。由此得出,利用二次规划方法求解得到的非负约束权重的组合预测模型在个人信用评估中是具有应用价值的结论。
With the development of consumer credit in domestic commercial banks, personal credit becomes more and more important. At present there is no perfect personal credit system established in China, and there are no scientific and reasonable methods or indicators applied in personal credit assessment. In this situation, researches on personal credit scoring are critical for the commercial banks to reduce the risk of personal credit and the ratio of non-performing loan. It also has a positive significance for the commercial banks to expand the consumer credit market which can accelerate and stabilize the development of the national economy.
Based on analysis of domestic and overseas in personal credit scoring, this dissertation firstly expatiates on the fundamental principles of the three statistical methods to be used in this domain and then establishes and tests the three models in personal credit scoring respectively. Then it elaborates the principles of combining forecasts as well as its methods of weights calculation. At last, after establishing a combined forecast model with non-negative combining weight constraint through multi-linear regression, logistic regression and Probit regression, this dissertation applies the combined model to personal credit scoring. In the weights calculation of the combination forecasting model, the dissertation uses the method Genetic Algorithms and introduces a new Neural Networks method of quadratic programming, which is more effective and reasonable. Through the contrast of the combining model with non-positive restriction on weights and the single ones in the final application, the result shows that the general accuracy of the models are all above 90%, while the effect of the combination forecasting model is better. At the same time, in the result of the combination forecasting model, the error rate of the first case is not the lowest, but its error rate of the second case has a comparative advantage. Therefore the combination forecasting model with non-negative combining weight constraint is generally better than the single ones. Through the contrast between the results of the two methods it shows that the weight of Multiple Linear Regression in quadratic programming is 0, so it is rejected. And the effect of classification based on the method of quadratic programming is better. Therefore it can be concluded that the combination forecasting model using Neural Networks of quadratic programming has an application value in personal credit scoring.
引文
1王长江,许纪校.建立个人信用制度,大力发展消费信贷.生产力研究. 2002, (1): 12~13
2姜楠华.关于我国个人信用制度理论与实践的探讨.银行与经济. 2002, (3): 28~29
3张兴夏.大力推进我国个人信用制度建设.发展研究. 2005, (10): 74~76
4董金玲.我国发展消费信贷的意义及思路.华东经济管理. 1999,13(3):54~55
5黄家全.发展消费信贷和需要解决的问题.中国经贸导刊. 1999, (4): 24~26
6詹漫丽.关于我国消费信贷发展的分析.辽宁经济. 2003, (3): 25
7戴根有,高材林.发展消费信贷是当前刺激经济的重要途径.中国金融. 1999, (4): 12~14
8熊其康.加快我国个人征信业发展的思考.金融理论与实践. 2004, (12): 22~24
9柯孔林,周春喜.商业银行信用风险评估方法研究述评.商业经济与管理. 2005, (6): 55~60
10熊其康.我国个人征信体系建设的目标规划及阶段构想.金融论坛. 2004, (9): 15~20
11李放.完善我国个人信用体系探析.新西部. 2008, (2): 81~82
12张维,李玉霜.商业银行信用风险分析综述.管理科学学报. 1998,1(3):20~27
13王春峰,万海晖,张维.商业银行信用风险评估及其实证研究.管理科学学报. 1998, 1(1): 68~72
14 Lyn C. Thomas. A Survey of Credit and Behavioral Scoring: Forecasting Financial Risk of Lending to Consumers. International Journal of Forecasting. 2000, (16): 149~172
15 Durand. D. Risk elements in consumer installment financing. National Bureau of Economic Research, New York. 1941:105~142
16 Eisenbeis, R. A. Pitfalls in the application of discriminant analysis in business, finance, and economics. The Journal of Finance. 1977, (32): 875~900
17 Eisenbeis, R. A. Problems in applying discriminant analysis in credit scoring models. Journal of Banking and Finance. 1978, (2): 205~219
18 Capon, N. Credit scoring systems: a critical analysis. Journal of Marketing. 1982, (46): 82~91
19 Rosenberg, E. and Gleit, A. Quantitative methods in credit management: a survey. Operations Research. 1994, (42): 589~613
20 Elizabeth Mays. Credit Risk Modeling: design and application. Fitzroy Dearborn Publishers. 1998:190~200
21石庆焱,靳云汇.个人信用评分的主要模型与方法综述.统计研究. 2003, (8): 36~39
22 Steenackers. A. M. J. Govaerts. A credit scoring model for personal loans. Insurance Mathematics and Economics. 1989, (98): 31~34
23 Grablowsky, B. J. and Talley, W. K. Probit and discriminant functions for classifying credit applicants: a comparison. Journal of Economics and Business. 1981, (33): 254~261
24 Mangasarian O L. Pseudoconvex functions J. SLAM Journal on Control, 1965, (3): 281~290
25 Freed, N., & Glover, F. A linear programming approach to the discriminant problem. Decision Sciences. 1981, (12): 68~74
26 Joachimsthaler, E. A. and A. Stam. Mathematical Programming Approaches for the Classification Problem in Two-Group Discriminant Analysis. Multivariate Behavioral Research. 1990, (25): 427~454.
27 Ziari, H. A., Leatham, D. J., Ellinger, P. N. Development of Statistical Discriminant Mathematical Programming Model via Resampling Estimation Techniques. American Journal of Agricultural Economic. 1997,79(4):1352~1362
28 T. M. Cover and P. E. Hart. Nearest neighbor patter n classification IEEE Transactions on Information Theory. 1967,13(1):22~45
29 Henley, W. E., and D. J. Hand. A k-nearest-neighbor classification for assessing consumer credit risk. The Statistician. 1996,45(1):32~63
30姜明辉等. K—近邻判别分析法在个人信用评估中的应用.数量经济技术经济研究. 2004, (2): 143~147
31 Lundy M.Cluster analysis in credit scoring. Credit Scoring and Credit Contro. New York: Oxford University Press. 1993:78~90
32 Sulin Pang, Bijun Hu and Yuanhuai Bai. Application of fuzzy cluster analysis in credit scoring. Journal of Systems Science and Information,2005,38(1):1027~1032
33 Makowski P. Credit Scoring Branches out. Credit World. 1985, (75): 30~50
34 Coffman, J. Y. The proper role of tree analysis in forecasting the risk behavior of borrowers. Management Decision Systems. Atlanta, MDS Reports. 1986, (3): 47~59
35 C. Carter, J. Catlett. Assessing Credit Card Applications Using Machine Learning. IEEE Expert. 1987:71~79
36方兆本等.消费者信用评估分析综述.系统工程. 2001,19(6):9~15
37张维,李玉霜,王春峰.递归分类树在信用风险分析中的应用.系统工程理论与实践. 2000, (3): 50~55
38王欢.基于分类树的我国商业银行个人信用评估方法研究.哈尔滨工业大学硕士学位论文. 2003, (7): 6~13
39 David West. Neural Network Credit Scoring Models. Computers & Operations Research. 2000, (27): 1131~1152
40王春峰等.商业银行信用风险评估:投影寻踪判别分析模型.管理工程学报. 2000,14(2):43~46
41赵静娴,杨宝臣.一种基于神经网络和决策树的信用评估新方法.武汉科技大学学报(社会科学版). 2005,7(2):36~39
42 Fogarty, T. C. and Ireson, N. I.Evolving Bayesian classifiers for credit control: a comparison with other machine learning methods. Presented to the 3rd IMA Conference on Credit Scoring and Credit Control. 1993, (5): 63~76
43 Clemen R.T. Combining forecasts: a review and annotated bibliography. International Journal of Forecasting, 1989, (5): 559~584
44陈旭鸣.现代信用风险管理模型发展研究.统计与决策. 2008, (9): 186~188
45马永开,唐小我,杨桂元.优性组合预测方法存在判别定理预测. 1995, (2): 57~59
46 Granger, C.W.J. and Ramanathan, R. Improved Methods of Combining Forecasts. Journal of Forecasting, 1984,3(2):197~204
47 Robert. T. Clemen. Linear Constraints and the Efficiency of Combined Forecasts. Journal of Forecasting. 1986, (5): 31~38
48丁岳维.组合预测模型的研究.西安公路交通大学学报. 1997,17(4):100~104
49 Xiaoping XUE, Wei BIAN. A Project Neural Network for Solving Degenerate Convex Quadratic Program. Neurocomputing. 2007, (70): 2449~2459
50周明,孙树栋.遗传算法原理及应用.国防工业工业出版社. 1999:4~54.
51李根义等.实数编码遗传算法优化的神经网络模型在岩溶水水位预报中的应用.南京大学学报(自然科学). 2001,37(3):323~327.
52杨桂元,唐小我.非负权重组合预测模型优化方法研究.数量经济技术经济研究. 1998, (3): 56~60
53唐小我,曾勇,曹长修.非负权重最优组合预测的迭代算法研究.系统工程理论方法应用. 1994,3(4):48~52
54 Zhu, Beling and Overstreet. A study in the combination of two consumer credit scores. Journal of Operations Research Society. 1999, (52): 974~980
55王春峰等.组合预测在商业银行信用风险评估中的应用.管理工程学报. 1999,13(1):5~8
56石庆焱.一个基于神经网络——Logistic回归的混合两阶段个人信用评分模型研究.统计研究. 2005, (5): 45~49
57唐小我等.现代组合预测和组合投资决策方法及应用.北京:科学出版社. 2003, 1: 178~201
2姜楠华.关于我国个人信用制度理论与实践的探讨.银行与经济. 2002, (3): 28~29
3张兴夏.大力推进我国个人信用制度建设.发展研究. 2005, (10): 74~76
4董金玲.我国发展消费信贷的意义及思路.华东经济管理. 1999,13(3):54~55
5黄家全.发展消费信贷和需要解决的问题.中国经贸导刊. 1999, (4): 24~26
6詹漫丽.关于我国消费信贷发展的分析.辽宁经济. 2003, (3): 25
7戴根有,高材林.发展消费信贷是当前刺激经济的重要途径.中国金融. 1999, (4): 12~14
8熊其康.加快我国个人征信业发展的思考.金融理论与实践. 2004, (12): 22~24
9柯孔林,周春喜.商业银行信用风险评估方法研究述评.商业经济与管理. 2005, (6): 55~60
10熊其康.我国个人征信体系建设的目标规划及阶段构想.金融论坛. 2004, (9): 15~20
11李放.完善我国个人信用体系探析.新西部. 2008, (2): 81~82
12张维,李玉霜.商业银行信用风险分析综述.管理科学学报. 1998,1(3):20~27
13王春峰,万海晖,张维.商业银行信用风险评估及其实证研究.管理科学学报. 1998, 1(1): 68~72
14 Lyn C. Thomas. A Survey of Credit and Behavioral Scoring: Forecasting Financial Risk of Lending to Consumers. International Journal of Forecasting. 2000, (16): 149~172
15 Durand. D. Risk elements in consumer installment financing. National Bureau of Economic Research, New York. 1941:105~142
16 Eisenbeis, R. A. Pitfalls in the application of discriminant analysis in business, finance, and economics. The Journal of Finance. 1977, (32): 875~900
17 Eisenbeis, R. A. Problems in applying discriminant analysis in credit scoring models. Journal of Banking and Finance. 1978, (2): 205~219
18 Capon, N. Credit scoring systems: a critical analysis. Journal of Marketing. 1982, (46): 82~91
19 Rosenberg, E. and Gleit, A. Quantitative methods in credit management: a survey. Operations Research. 1994, (42): 589~613
20 Elizabeth Mays. Credit Risk Modeling: design and application. Fitzroy Dearborn Publishers. 1998:190~200
21石庆焱,靳云汇.个人信用评分的主要模型与方法综述.统计研究. 2003, (8): 36~39
22 Steenackers. A. M. J. Govaerts. A credit scoring model for personal loans. Insurance Mathematics and Economics. 1989, (98): 31~34
23 Grablowsky, B. J. and Talley, W. K. Probit and discriminant functions for classifying credit applicants: a comparison. Journal of Economics and Business. 1981, (33): 254~261
24 Mangasarian O L. Pseudoconvex functions J. SLAM Journal on Control, 1965, (3): 281~290
25 Freed, N., & Glover, F. A linear programming approach to the discriminant problem. Decision Sciences. 1981, (12): 68~74
26 Joachimsthaler, E. A. and A. Stam. Mathematical Programming Approaches for the Classification Problem in Two-Group Discriminant Analysis. Multivariate Behavioral Research. 1990, (25): 427~454.
27 Ziari, H. A., Leatham, D. J., Ellinger, P. N. Development of Statistical Discriminant Mathematical Programming Model via Resampling Estimation Techniques. American Journal of Agricultural Economic. 1997,79(4):1352~1362
28 T. M. Cover and P. E. Hart. Nearest neighbor patter n classification IEEE Transactions on Information Theory. 1967,13(1):22~45
29 Henley, W. E., and D. J. Hand. A k-nearest-neighbor classification for assessing consumer credit risk. The Statistician. 1996,45(1):32~63
30姜明辉等. K—近邻判别分析法在个人信用评估中的应用.数量经济技术经济研究. 2004, (2): 143~147
31 Lundy M.Cluster analysis in credit scoring. Credit Scoring and Credit Contro. New York: Oxford University Press. 1993:78~90
32 Sulin Pang, Bijun Hu and Yuanhuai Bai. Application of fuzzy cluster analysis in credit scoring. Journal of Systems Science and Information,2005,38(1):1027~1032
33 Makowski P. Credit Scoring Branches out. Credit World. 1985, (75): 30~50
34 Coffman, J. Y. The proper role of tree analysis in forecasting the risk behavior of borrowers. Management Decision Systems. Atlanta, MDS Reports. 1986, (3): 47~59
35 C. Carter, J. Catlett. Assessing Credit Card Applications Using Machine Learning. IEEE Expert. 1987:71~79
36方兆本等.消费者信用评估分析综述.系统工程. 2001,19(6):9~15
37张维,李玉霜,王春峰.递归分类树在信用风险分析中的应用.系统工程理论与实践. 2000, (3): 50~55
38王欢.基于分类树的我国商业银行个人信用评估方法研究.哈尔滨工业大学硕士学位论文. 2003, (7): 6~13
39 David West. Neural Network Credit Scoring Models. Computers & Operations Research. 2000, (27): 1131~1152
40王春峰等.商业银行信用风险评估:投影寻踪判别分析模型.管理工程学报. 2000,14(2):43~46
41赵静娴,杨宝臣.一种基于神经网络和决策树的信用评估新方法.武汉科技大学学报(社会科学版). 2005,7(2):36~39
42 Fogarty, T. C. and Ireson, N. I.Evolving Bayesian classifiers for credit control: a comparison with other machine learning methods. Presented to the 3rd IMA Conference on Credit Scoring and Credit Control. 1993, (5): 63~76
43 Clemen R.T. Combining forecasts: a review and annotated bibliography. International Journal of Forecasting, 1989, (5): 559~584
44陈旭鸣.现代信用风险管理模型发展研究.统计与决策. 2008, (9): 186~188
45马永开,唐小我,杨桂元.优性组合预测方法存在判别定理预测. 1995, (2): 57~59
46 Granger, C.W.J. and Ramanathan, R. Improved Methods of Combining Forecasts. Journal of Forecasting, 1984,3(2):197~204
47 Robert. T. Clemen. Linear Constraints and the Efficiency of Combined Forecasts. Journal of Forecasting. 1986, (5): 31~38
48丁岳维.组合预测模型的研究.西安公路交通大学学报. 1997,17(4):100~104
49 Xiaoping XUE, Wei BIAN. A Project Neural Network for Solving Degenerate Convex Quadratic Program. Neurocomputing. 2007, (70): 2449~2459
50周明,孙树栋.遗传算法原理及应用.国防工业工业出版社. 1999:4~54.
51李根义等.实数编码遗传算法优化的神经网络模型在岩溶水水位预报中的应用.南京大学学报(自然科学). 2001,37(3):323~327.
52杨桂元,唐小我.非负权重组合预测模型优化方法研究.数量经济技术经济研究. 1998, (3): 56~60
53唐小我,曾勇,曹长修.非负权重最优组合预测的迭代算法研究.系统工程理论方法应用. 1994,3(4):48~52
54 Zhu, Beling and Overstreet. A study in the combination of two consumer credit scores. Journal of Operations Research Society. 1999, (52): 974~980
55王春峰等.组合预测在商业银行信用风险评估中的应用.管理工程学报. 1999,13(1):5~8
56石庆焱.一个基于神经网络——Logistic回归的混合两阶段个人信用评分模型研究.统计研究. 2005, (5): 45~49
57唐小我等.现代组合预测和组合投资决策方法及应用.北京:科学出版社. 2003, 1: 178~201