Applied Research of Genetic Algorithm in Personal Credit Risk Combined Assessment

Transcription

1 Manageent Science and Engineering Vol. 7, No. 3, 2013, pp DOI: /j.se X ISSN [Print] ISSN X [Online] Applied Research of Genetic Algorith in Personal Credit Risk Cobined Assessent SHUAI Li [a] ; LI Tingting [a] ; XU Chao [a] ; ZHOU Zongfang [a],* [a] School of Manageent and Econoics, University of Electronic Science and Technology of China, Chengdu, China. * Corresponding author. Supported by the Natural Science Foundation of China ( ), the Special Research Foundation of Ph.D Progra of China ( ), and Sichuan Province Science and Technology Support Project (2012SZ0001). Received 17 June 2013; accepted 16 August 2013 Abstract With the increasing scale of individual credit consuption, the individual credit risk assessent has becoe ore and ore iportant. This paper selected 640 saples fro the Gerany personal credit database as study object. First, this preliinary screened the priitive indexes, and then used saple classification accuracy as fitness function, aking cobined assessent odel based on linear regression and logistic regression through genetic algorith. The results showed that the cobined assessent odel based on genetic algorith had higher accuracy copared to a single odel, and cobined assessent odel based on the least su of square error had an advantage in the individual credit risk assessent over the others. Key words: Personal credit risk assessent; Genetic algorith; Logistic regression; Cobined assessent SHUAI Li, LI Tingting, XU Chao, ZHOU Zongfang (2013). Applied Research of Genetic Algorith in Personal Credit Risk Cobined Assessent. Manageent Science and Engineering, 7 (3), Available fro: URL: index.php/se/article/view/j.se x DOI: INTRODUCTION Credit risk, also known as default risk, refers to the potential losses that the bank ight suffer fro the unwillingness or incapability of the borrower to fulfill the contract because of various reasons (Zhou et al., 2010). Causes for individual credit risk can be concluded into the following aspects: asyetric inforation, the borrower s oral, repayent will and ability. Personal credit assessent ethods including using rigorous scientific analysis ethods, taking into account the inner and outer, subjective and objective environent that influence the individual and the faily, aking coprehensive judgent and assessent to their ability to fulfill the econoic coitents, and using certain sybols to indicate their credit state (Huang, Zhou, & Yu, 2010). The existing personal credit assessent ethods are ainly divided into two classes, one is the ethod based on statistic odel, such as ultiple discriinant analysis, linear regression, logistic regression; the other is nonparaetric estiation and artificial intelligence ethod, including neural network, classification tree, and genetic algorith etc. Research on personal credit assessent is continuing developing and aturing at hoe and abroad. For exaple, Liang, Guo, Li, & Fang (2002) analyzed the ain cause of the rapid developent of odern credit risk odel, coparatively analyzed the theory, advantage and disadvantage of each odel; Shi & Jin (2004) coparatively analyzed the application of various ethods in doestic sall saple data; Jiang & Chen (2006) provided the LS estiation and hypothesis test of the weight of cobined forecast odel, fro statistic aspect; Ma & Tang (1998) described and analyzed the accuracy feature of the linear cobined forecast odel, based on the absolute error series of the linear cobined odel; Jiang (2006) took the idea of cobined forecast, proposed the forecasting ethod of cobining the ultiple linear regression and logistic regression by using RBF neural network, and applied it in personal credit assessent; Chen & Xu (2000) applied and copared three cobined 81 Copyright Canadian Research & Developent Center of Sciences and Cultures

2 Applied Research of Genetic Algorith in Personal Credit Risk Cobined Assessent forecast odel: linear cobination, variable weights cobination, and non-linear cobination; Fogarty & Ireson (1993) were two pioneer scholars in applying genetic algorith in scoring; Zhu & Feng (2003) proposed the ethod to deterine the weight factor of the cobined forecast ethod based on genetic algorith. This paper select 640 Geran personal credit saple data as research object, firstly, this preliinary screens the priitive indexes, then establish two single statistic odel: linear regression and Logistic regression, and build the personal credit cobined assessent odel, finally, analyze the epirical results. 1. THE SELECTION AND QUANTIFICATION OF PERSONAL CREDIT ASSESSMENT INDEXES The personal credit assessent indexes that this paper selects conclude the following three aspects. (1) The naturel condition of the individuals, such as age, sex, arriage, education, housing and vehicle condition. (2) The financial condition of the individuals, such as profession and occupation, job and title, years of working, onthly incoe, annual faily revenue, onthly payent to onthly disposable incoe rate. (3) Social condition of individuals, on one hand, it is about the status of the business aong the individual and the bank and other financial institutions, ainly includes: Bad credit record, su of business with the bank, saving account in the bank, default record, year of credit record, on the other hand, it is about the status of the business aong the individual and the non-bank financial institutions, ain includes: insurance, tax evasion, tax loophole record, record of alicious default on utilities, and judicial, public records. Due to the difficulty of collecting the original personal credit assessent data and files in the doestic, this paper selected 1000 personal credit saple data of Geran as the study objects, which have 20 attributes indexes, according to the Chinese context, the indexes are finally deterined as following table shows: Table 1 Selection and Quantification of Personal Credit Assessent Indexes Indexes Variable Definition Age X 1 Marriage X 2 1 = Single; 2 = Married Supporting faily ebers X 3 Working condition X 4 1 = Uneployed/anual workers, non-resident; 2 = Non-proficient worker, resident; 3 = Proficient worker/officer; 4 = Manager/independent entrepreneurs Year of working X 5 1 = Uneployed; 2 = Less than 1 year; 3 = 1-4 years; 4 = 4-7 years; 5 = More than 7 years Housing condition X 6 1 = Rent; 2 = Owned; 3 = Free housing Year of living in current house Installent to deposable disposable incoe rate X 7 X 8 Assets X 9 1 = Real estate; 2 = If not 1: agreeent of public construction savings/life insurance; 3 = If not 2: autoobile or other; 4 = Vain Current payent account status X 10 1=Less than 0 ark; 2 = dollar; 3 = More than 200 dollars or salary contract has been signed for at least a year; 4 = No payent account Rest plan for the installent X 11 1 = Bank; 2 = Stock; 3 = No Debt aount X 12 Saving account/bonds X 13 1 = Less than 100 ark; 2 = dollar; 3 = dollar; 4 = More than 1000 dollar; 5 = No saving account/bonds Loan period X 14 Credit record X 15 0 = No bad credit record; 1 = Has overdue payent record/other bad credit record; 2 = Overdue payent; 3 = Has late payent record; 4 = No credit record/credit record is no in this bank Existing loan project nuber in this bank X 16 Other note debtor/guarantor X 17 1 = No; 2 = Joint applicants; 3 = Secured Saple classification Y 0 = Bad credit; 1 = Good credit Copyright Canadian Research & Developent Center of Sciences and Cultures 82

3 SHUAI Li; LI Tingting; XU Chao; ZHOU Zongfang (2013). Manageent Science and Engineering, 7(3), IDEA OF BUILDING THE COMBINED ASSESSMENT MODEL BASED ON GENETIC ALGORITHM Cobined assessent is the weighted cobination of different assessent odel, and it has unique effect in iproving the accuracy and robustness of the assessent, which leads to its wide application and assive study to it. The theory of linear cobination assessent is as follows: We presue there are assess ethod to one proble, f it is value of the i th kind of assess ethod for the t th person (i=1,2...,;t=1,2,...,n), w i represents the weight of i th assess ethod, f t represents the value of cobined assessent for the t th person, then the atheatical odel of the linear cobination assessent is as follow: ft = / i = 1 wf i it st, / wi = 1, t = 1,2,..., n (1) i = 1 The key to cobined assessent odel is to solve the weight of it, this paper use genetic algorith to get the weight w i. Genetic Algorith (GA) initially proposed by Holland (1975), which is a heuristic optiization algorith to a siulated biological population genetic and evolutionary echanis, the search is guided by the fitness value of the individual (Lei, Zhang & Li, 2004). The selection of the fitness function and the genetic operator (selection operator, cross operator, utation operator) is the core of the genetic algorith. GA deterines the search direction by choosing the operator to weed out the poor individual of the group, and the selection of the operator is deterined by the fitness value, then carry out the operation of cross and utation, finally get the optiu solution, soe key steep are as follow: (1) The coding of the genetic algorith and the setting of the initial group Coding is the first proble that needs to be solved before applying the genetic algorith, usually there two coding ethod of coding: binary coding (0,1 coding) and floating nuber coding. Binary coding is the ain coding way in genetic algorith, because the paraeters that need to be deterined in constructing the cobined assessent odel are few, and the value range of it is sall, this paper use binary coding. When the nuber of the group is sall it can iprove the running speed in the cost of reducing the diversity of the group, and leading to preature convergence of the genetic algorith; When the nuber of the group is large, it will reduce the efficiency. Generally, proposed group scale is This paper select two of the to construct a cobined predict odel, with 2 paraeters to be deterined, thus, the initial group scale is set 20, and the generation of the group evolution is set 100. (2) Selection of fitness function Fitness value easures the adaptation ability of the individual in evolution. Individuals with high fitness value is ore likely to survive, and produce offspring with high adaptation ability through genetic echanis, otherwise, individuals with low fitness value will gradually be weed out. This paper use classification accuracy to calculate the fitness function: fit =1, n is the nuber of the n saple, is isclassified nuber. (3) Selection of the three operators The selection of operator is built based on the valuation of the adaptation ability of individuals. Its ain purpose is to avoid issing gene, and to iprove the overall convergence, and operating speed. This paper use proportional selection ethod, first calculate the fitness function value of each individual, the sort the, and select individual according the following probit: fiti pi = N (2) fit i= 1 Aong the, fit i is the fitness value of individual i, p i is the probability of each individual to be selected, N is the scale of the group, this paper set 20. Crossover operation is to exchange part of the gene of two pared chroosoe according to soe ethod, and for two new individual. Crossover operation includes single point crossover, ulti-point crossover, balanced crossover, and then exchange the gene after that point, the probability of crossover is generally set , this paper choose The echanis of utation operator is siilar to gene utation, which is one of the ethods to produce new individual. This paper adopts the basic utation operator, to ake utation operation of the value of one or soe gene, randoly appointed by the utation probability of individual coding. Mutation probability is norally , this paper chooses BUILDING AND APPLICATION OF THE MODEL 3.1 Selection and Standardization of the Saple Data This paper selected 640 saple data of Gerany personal credit as the study object, in which 340 saples were classified into class 1 (good credit), and 300 saples into class 2 (bad credit). Every saple included 17 attributes indexes. Then we noralized the indexes, and the personal data was classified into continues data and rando data, for each of the needed different ethods. As to discrete data, in-ax noralization ethod is used to precede the original data, and to ake the into the district [0, 1]: xij - in xij x' ij = (3) ax xij - in xij i 83 Copyright Canadian Research & Developent Center of Sciences and Cultures

4 Applied Research of Genetic Algorith in Personal Credit Risk Cobined Assessent Aong the, x' ij is the new attribute value of indicator i of saple j, x ij is the origin attribute value of the indicator i of saple j, in x ij is the iniu of all the saple attributes indexes value of indicator i, ax x ij is the axiu of all the saple attributes indexes value of indicator. As to the saple date that this paper used, age, loan aount, and loan period, which were continuous data, by observing their distribution ap, they were found 2 to be siilar to Gaussian distribution, x ~ N( µ, σ ), converting the into (0,1) by ethod of standardization: x µ x = Φ( ) (4) σ U^xh is the Gaussian distribution. Aong the, Through this converting, we got to probability according to the indicator. This paper uses stratified sapling, in order to reduce influence to the odel classification brought by the uneven of the data, the nuber of each kind of saple were equal. Aong then, the training saple and the testing saple all included 170 good saples and 150 bad saples. 3.2 Single Statistical Model Multiple linear regression Multiple linear regression has a strict requireent for the distribution of the data, however, when the saple is large, valuation odel eliinated the ulticollinearity between explanatory variables is efficiently explicable, the variables in the odel are of econoic iportance. To satisfy the requireent that there are no ulticollinearity aong variables, this paper used gradually stepwise to eliinate effect brought by the ulticollinearity between variables. The final explanatory variables were x 5,x 9,x 10,x 12,x 13,x 14,x 15, and the result of linear regression was: f1t = x5t x9t x12t (5) x13t x14t x15t Using the static software to exa the significance of the paraeter and the whole function, the result proved their significance Logistic regression odel Logistic regression has coparatively advantage in proceeding data, and is robust. The ethod of variable screen was to backward conditional screen, according to proposed paraeter ake the likelihood ratio probability test, the obtained Logistic regression function was: f2 t 1n x x x f = t (6) x x x15 Aong the, f 2t was the probability of person t of good credit. 3.3 Linear Cobined Predict Model Based on Miniu Error Square To copare the valuation effect of cobined valuation odel based on genic algorith, first, we built the linear cobined odel: ft = w1f1t+ w2f2t st, w1+ w2 = 1 (7) The weight w 1,w 2 ay be negative. The cobined predict odel based on iniu error square was: ft = f1t f2t (8) 3.4 Cobined Valuation Model Based on Genic Algorith Genic algorith evolved 100 generation, finally we get the weight were and , the fitness value now was , which eant the accuracy rate of this odel in classification was 89.77%, cobined valuation odel was: ft = f1t f2t (9) Aong the, f 1t,f 2t were the valuation result of person t in linear regression odel and logistic regression odel. Apply the above odels in saple test, using 0.5 as Classification boundaries, which eant the value result was higher than 0.5, then the credit was classified good, the value result was lower than 0.5, the credit was classified bad (Ma & Tang, 1998), the classification result was as the following table: Table 2 Coparison of the Classification Results of Single Model and Cobined Valuation Model Model Assessed value Saple nuber Accuracy Error rate 1 (good) 0 (bad) Multiple linear regression odel Logistic regression odel Cobined valuation odel based on iniu error square Cobined valuation odel based on genic algorith 1 (good) % 10.00% 0 (bad) % 17.33% Total classification percentage % 13.43% 1 (good) % 8.82% 0 (bad) % 13.33% Total classification percentage % 10.93% 1 (good) % 8.82% 0 (bad) % 11.33% Total classification percentage % 10.00% 1 (good) % 7.64% 0 (bad) % 10.66% Total classification percentage % 9.06% Copyright Canadian Research & Developent Center of Sciences and Cultures 84

5 SHUAI Li; LI Tingting; XU Chao; ZHOU Zongfang (2013). Manageent Science and Engineering, 7(3), CONCLUSION Copare the classification result of cobined odel and single odel. Table 2 shows that, both the two of the cobined odel were better than single odel in general classification accuracy, and they had iproveent in reducing false accept rate, which eant that the cobined valuation odel were superior than single odel in classification accuracy. Copare the cobined odel based on iniu error square and the cobined odel based on genic algorith. Table 2 showed that the latter were better than the forer, in both accuracy, and the Error Type I (reject the truth) and Error type II (accept the false), especially in the Error type II. Generally speaking, regarding to the classification, in personal credit classification, the cobined odel was better than the single odel, especially in avoiding the Error type II (accept the false). The cobined valuation odel based on genic algorith was better than the cobined valuation odel based on iniu error square. REFERENCES Chen, H. Y., & Xu, Y. S. (2000). The estiation of weight of cobined prediction and its significance test. Operations Research and Manageent Science, (2), Fogarty, T. C., & Ireson, N. I. (1993). Evolving Bayesian classifiers for credit control: A coparison with other achine learning ethods. Proceedings of the 3rd IMA Conference on Credit Scoring and Credit Control (Vol.5, pp.63-76). Huang, H. Z., Zhou, Z. F., & Yu, J. K. (2010). ILMBP neural network odel and its application in personal credit valuation. Managerialist, (10). Jiang, M. H. (2006). Research of the cobination forecast ethod of individual credit evaluation for coercial bank (Doctoral dissertation). Retrieved fro CNKI ( cnki.co.cn/article/cdmd ht). (In Chinese). Jiang, M. H., & Chen, Y. F. (2006). Cobining forecasts of personal credit scoring based on RBF neural network. Journal of Harbin Engineering University, 27(z1). (In Chinese). Lei, Y. J., Zhang, S. W., & Li, X. W. (2004). MATLAB genetic algorith toolbox and its application. Xi an: Xidian University Press. (In Chinese). Liang, S. D., Guo, B., Li, Y., & Fang, Z. B. (2002). Coparative analysis of credit risk odel. China Manageent Science, 10(1), (In Chinese). Ma, Y. K., & Tang, X. W. (1998). Research of the optiization of linear cobined prediction odel. Systes Engineering- Theory & Practice, (9), (In Chinese). Shi, Q. Y., & Jin, Y. H. (2004). Coparative research of the application of ultiple personal credit rating odel in China. Statistic Research, (6), (In Chinese). Zhou, Z. F., et al. (2010). The study of the evolution echanis and valuation ethod of eerging technology enterprise. Beijing: Science Press. Zhu, X. D., & Feng, T. J. (2003). Personal credit valuation based on GA neural network. Systes Engineering-Theory & Practice, (12), (In Chinese). 85 Copyright Canadian Research & Developent Center of Sciences and Cultures