WO2019140675A1 - 基于逼近理想点违约鉴别能力最大的信用评级最优权重向量的方法 - Google Patents

基于逼近理想点违约鉴别能力最大的信用评级最优权重向量的方法 Download PDF

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WO2019140675A1
WO2019140675A1 PCT/CN2018/073568 CN2018073568W WO2019140675A1 WO 2019140675 A1 WO2019140675 A1 WO 2019140675A1 CN 2018073568 W CN2018073568 W CN 2018073568W WO 2019140675 A1 WO2019140675 A1 WO 2019140675A1
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defaulting
score
credit
enterprise
ideal point
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PCT/CN2018/073568
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French (fr)
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迟国泰
李鸿禧
周颖
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大连理工大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N5/00—Computing arrangements using knowledge-based models
    • G06N5/01—Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
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    • G06F16/21—Design, administration or maintenance of databases
    • G06F16/215—Improving data quality; Data cleansing, e.g. de-duplication, removing invalid entries or correcting typographical errors
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
    • G06F16/25—Integrating or interfacing systems involving database management systems
    • G06F16/258—Data format conversion from or to a database
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N20/00—Machine learning
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N5/00—Computing arrangements using knowledge-based models
    • G06N5/04—Inference or reasoning models
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q30/00—Commerce
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
    • G06Q40/03—Credit; Loans; Processing thereof

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  • the invention provides a method for determining the optimal weight vector of the credit rating index, and the credit rating system has the largest discriminating ability, and belongs to the credit service technology field.
  • Credit ratings have an extremely important impact on today's economy and society. Whether it is a sovereign credit rating, a corporate credit rating, a bank credit rating, or a personal credit rating. If the credit rating results are unreasonable and the risk of default cannot be accurately assessed, investors and the public will be misled. Small enough to lead to the bankruptcy of banks and enterprises, and to the financial crisis, and even the entire economic and social disorder. A reasonable credit rating system must have strong default identification capability, which can effectively distinguish default customers from non-default customers and accurately identify customers with high default risk.
  • Empowering indicators and calculating credit scores are an important part of the credit rating.
  • the credit evaluation equation is a function of the index data and the weight vector, so the size of the index weight, the structure of the weight vector and the quality of the rating result are inextricably linked.
  • the first is subjective empowerment based on expert judgment.
  • the "Enterprise Credit Rating Method” of the Intellectual Property Office of the People's Republic of China with the patent number of 201710669426.X and the "A Credit Evaluation Method Based on the Analytic Hierarchy Process” with the patent number 201410334653.3 use the AHP AHP to determine the multi-level according to the expert judgment matrix. Evaluate the weight of the indicator and calculate the corporate credit score.
  • the second is objective weighting based on methods such as measurement statistics and artificial intelligence.
  • the People's Republic of China Intellectual Property Office patent number is 201710428343.1 "A method, device and electronic equipment for employee credit evaluation and application” to establish a logistic regression model of credit rating, using the maximum likelihood estimation algorithm to calculate the weight corresponding to each indicator .
  • the “Learning-based Enterprise Credit Evaluation Method” of the Intellectual Property Office of the People's Republic of China with patent number 201511031192.3 uses the deep learning algorithm to adjust the index weights to achieve consistency in cognition and generation.
  • the "Consumer behaviors at lender level” of the USPTO 41117586 uses statistical regression analysis to weight indicators to evaluate consumer credit risk.
  • the "Methods and systems for automatically generating high quality adverse action notifications" of the World Intellectual Property Organization patent number WO/2014/121019 uses genetic algorithms to authorize the construction of a credit evaluation model to identify the lender's default risk.
  • the third is the subjective and objective combination weighting method.
  • the patent number of the Intellectual Property Office of the People's Republic of China is 201611001902.2, "A method and system for enterprise credit evaluation based on subjective and objective weighted multi-model combination verification".
  • the method of subjective and objective weight assignment is combined with the index to conduct enterprise credit evaluation.
  • the above subjective empowerment does not reflect the relationship between the index weight and the default status, and does not reflect the relationship between the rating result and the true default status.
  • the credit rating is determined by the credit rating of the customer's credit score. If the internal relationship between the weight vector and the accuracy of the rating result is separated, then the weight determined is not optimal.
  • the invention approximates the lowest score by the rating result of the bad customer of the default, and the method of the non-defaulting good customer approaching the highest score approximates the ideal point to construct the multi-objective planning function, under the extreme condition that the default of the credit score has the largest discriminating ability, Reverse the optimal weight of a set of credit evaluation equations. Ensuring the credit rating result, that is, the size of the credit rating equation, can significantly distinguish between default and non-defaulting customers.
  • the positive ideal point is defined as the maximum weighted score of each index, indicating the highest score;
  • the negative ideal point is defined as the minimum of each index. The value-weighted score indicates the lowest score;
  • the Euclidean distance algebra and the minimum of the non-defaulting enterprise's credit score to the positive ideal point, the Euclidean distance algebra of the defaulting enterprise's credit score to the negative ideal point and the minimum is the first objective function; the "non-defaulting enterprise score and the positive ideal point"
  • the distance of the distance is the smallest, and the degree of dispersion of the distance between the defaulting firm and the negative ideal point is the second objective function.
  • the multi-objective programming function is constructed, and the optimal weight of a set of credit evaluation equations is reversed to ensure credit.
  • the evaluation result of the evaluation equation is that the non-defaulting enterprise scores the highest, while the defaulting enterprise scores the lowest, minimizing the overlap between the two types of samples;
  • Step 1 Construct a credit risk assessment indicator system
  • the redundant indicators reflecting the information duplication are eliminated from the sea selection index. Then, the index of the residual status of the default status is selected from the index system retained by the above-mentioned screening through Probit regression, and the credit risk evaluation is obtained.
  • Indicator system
  • Constructing a credit risk evaluation index system is the basis for the follow-up empowerment to construct a credit evaluation equation, and has several methods for determining;
  • the indicator data with significant distinguishing ability in step 1 and the default status of the customer are imported into the Excel file; the imported indicator data is standardized and converted into [0, 1] Data within the interval, eliminating the effects of the dimension;
  • Step 3 Build the distance function
  • Step 3.1 Determine the positive and negative ideal points:
  • Step 3.2 build the distance function: build a non-defaulting enterprise credit score Distance function to positive ideal point S + Where w j is the index weight and the decision variable to be sought. Is the indicator standardization data of the non-defaulting enterprise in step 2, and S + is the positive ideal point determined in step 3.1;
  • Step 4 Build the first objective function
  • n 0 is the number of non-defaulting enterprises
  • C is the penalty coefficient
  • n 1 is the number of defaulting enterprises
  • the formula (1) is used as the first objective function to construct the planning model, and the optimal weight vector of a set of credit rating equations is reversed.
  • the evaluation result of the credit evaluation equation is guaranteed to make the non-defaulting enterprise's score the highest and the defaulting enterprise's score the lowest. Credit scores can significantly distinguish between default and non-defaulting customers;
  • Step 5 Build the second objective function
  • the difference between the first objective function and the second objective function is that the first objective function is to ensure that the non-defaulting enterprise has the highest score, while the defaulting enterprise has the lowest score, and the second objective function is to make the score of the defaulting company and the non-defaulting enterprise cross.
  • Minimum overlap
  • Step 6 Build the constraints
  • a multi-objective programming model is constructed by the first objective function of step 4, the second objective function of step 5, and two constraints; the set of optimal weight vectors of the credit evaluation equation is reversed, so that the credit evaluation result is obtained.
  • the scores of non-defaulting enterprises are gathered near the positive ideal point, and the scores of defaulting enterprises gather near the negative ideal point, which maximizes the score gap between the two types of enterprises;
  • Step 7 Solve the optimal weight vector
  • the first objective function formula (1) and the second objective function formula (2) in the multi-objective programming model are linearly weighted according to a ratio of 1:1 to obtain a single objective function programming model;
  • Step 8 Calculate the credit evaluation score
  • step 4 Using the weight of step 4 to solve the result w j * , the index normalized data x ij of step 2, construct a credit evaluation equation by linear weighting, and calculate the credit score.
  • the present invention provides a method for deducting a set of optimal weight vectors based on credit score default discriminating ability.
  • the weighting method of the invention can ensure the credit score of the evaluation equation, satisfy the highest credit score of the non-defaulting enterprise, and the lowest credit score of the defaulting enterprise, so that the credit score is the largest to separate the defaulting enterprise from the non-defaulting enterprise.
  • the weighting method of the present invention can ensure the credit score of the evaluation equation, and the two types of enterprises satisfying the non-default and default have the smallest overlap of the scores and the least possibility of mixing, so that the “default is non-default” and “non-default judgment” The possibility of misjudgment for breach of contract is minimized.
  • the credit score is calculated by using the inverse weight of the present invention to more reasonably evaluate the default risk of a loan or debt. It can enable commercial banks, creditors, the public and other investors to understand the default status of bonds, loans and other debts, and make investment decisions.
  • the weighting model of the present invention has the function of index selection.
  • Figure 1 is a schematic diagram of the credit scores of two types of enterprises, default and non-default.
  • the solid circle represents the credit score interval of the non-defaulting enterprise
  • the dotted circle represents the credit score interval of the defaulting enterprise
  • the middle part is the overlapping overlapping interval of the two.
  • the geometric meaning of the first objective function formula (1) is such that the solid circle in which the non-defaulting enterprise in Fig. 1 is located is closest to the right ideal point S + on the right side, and the dotted circle in which the defaulting enterprise is located is closest to the negative ideal point S on the left side - .
  • the geometrical meaning of the second objective function formula (2) is to minimize the overlap region in the middle of Fig. 1.
  • Figure 2 is the principle of weighting based on the ability to approximate the ideal point default.
  • An object of the present invention is to provide an optimum weight determining method which maximizes the default discrimination ability of a credit rating result.
  • the Euclidean distance algebra with the credit score of the non-defaulting enterprise to the positive ideal point and the Euclidean distance algebra of the minimum, default enterprise credit score to the negative ideal point and the minimum is the first objective function.
  • the minimum degree of dispersion between the “non-defaulting enterprise score and the positive ideal point” and the “distance between the defaulting enterprise and the negative ideal point” are the second objective function, and the multi-objective programming function is constructed to reverse the set.
  • Step 1 Construct a credit risk assessment indicator system.
  • the partial correlation analysis is used to eliminate redundant indicators reflecting information duplication in the sea selection index. Then, through Probit regression, from the above-mentioned index system retained after screening, the indicators that have significant ability to distinguish the default status are selected, and the credit risk evaluation index system is obtained.
  • the credit risk assessment indicator system is shown in the second column of Table 1.
  • the construction of the credit risk evaluation index system is the basis for the follow-up empowerment to construct the credit evaluation equation, and there are several methods for determining.
  • Step 2 Import the data.
  • Import the indicator data the customer's default status (default customer 1, non-default customer 0) into the Excel file.
  • the imported indicator data is standardized and converted into data in the interval [0, 1] to eliminate the influence of the dimension.
  • Step 3 Establish a multi-objective planning model.
  • Step 3.1 Determine the positive and negative ideal points.
  • Step 3.2 Build the distance function. Standardize data for indicators of non-defaulting companies in step 2
  • Negative ideal point S - 0 in step 3.1, substituted into the formula Get the distance function of the default corporate credit score to the negative ideal point.
  • Step 4 Build the first objective function.
  • n 0 is the number of non-defaulting enterprises
  • n 1 is the number of defaulting enterprises
  • C is the penalty coefficient introduced to solve the sample imbalance problem
  • C n 0 / n 1 .
  • the planning model is constructed with objective function 1, and the optimal weight vector of a set of credit rating equations is reversed.
  • the evaluation result of the guaranteed credit evaluation equation makes the non-defaulting enterprise's score the highest and the defaulting enterprise's score the lowest.
  • the geometric meaning is that the solid circle of the non-defaulting enterprise in Figure 1 is closest to the positive ideal point S + on the right, and the dotted circle where the defaulting enterprise is located is closest to the negative ideal point S - on the left.
  • Step 5 Construction of the second objective function.
  • the objective function 1 differs from the objective function 2 in that the objective function 1 is to ensure that the non-defaulting enterprise has the highest score and the defaulting enterprise has the lowest score, and the objective function 2 is to minimize the overlapping of the scores of the defaulting enterprise and the non-defaulting enterprise.
  • Step 6 Construction of constraints.
  • This patent constructs a multi-objective programming model through the objective function of step 4, the objective function of step 5, and the two constraints of step 6. Reverse the set of optimal weight vectors of the credit evaluation equation to ensure the size of the credit rating equation and the customers who can significantly distinguish between defaults.
  • the rating result of the guaranteed credit rating equation is that the non-defaulting enterprise scores the highest, while the defaulting enterprise scores the lowest, minimizing the overlap between the two types of samples.
  • the principle is shown in Figure 2.
  • Step 7 Solve the optimal weight vector.
  • the first objective function obj1 and the second objective function obj2 in the multi-objective programming model are linearly weighted according to a ratio of 1:1 to obtain a single objective function.
  • the constraints are unchanged, as described in step 6.
  • the result of solving the weight is directly displayed on the Excel interface.
  • Step 8 Calculate the credit rating score.
  • the index normalized data x ij of step 2 constructs a credit evaluation equation by linear weighting, and calculate the credit score.
  • the weighting method of the present invention is compared with the existing weighting method of the existing research.
  • the third column in Table 2 is the weight obtained by the present invention, the fourth column is the weight obtained based on the coefficient of variation method, and the fifth column is the weight obtained based on the F statistic.
  • the J-T non-parametric test statistic is used to test the credit score default identification ability obtained after empowerment. The larger the J-T test statistic, the more clearly the credit score can distinguish between default and non-default customers, and the greater the default identification ability of the weight vector.
  • the present invention has various specific embodiments, and all the technical solutions formed by the equivalent replacement or equivalent transformation based on the credit classification optimal credit classification method according to the present invention are all in the present invention. Within the scope of protection.

Abstract

本发明提供了一种基于逼近理想点违约鉴别能力最大的信用评级最优权重向量的确定方法，属于信用服务技术领域。以非违约企业的信用得分到正理想点的欧式距离代数和最小、违约企业的信用得分到负理想点的欧式距离代数和最小为第一个目标函数。以"非违约企业得分与正理想点的距离"的离散程度最小、"违约企业得分与负理想点的距离"的离散程度最小为第二个目标函数，构建多目标规划函数，反推一组信用评级方程的最优权重；确保信用评级方程得分的大小、能够显著区分违约与否的客户。保证信用评级方程的评级结果为非违约企业得分最高、而违约企业得分最低，最大程度地减少两类样本之间的交叉重叠。

Description

基于逼近理想点违约鉴别能力最大的信用评级最优权重向量的方法 技术领域
本发明提供了一种信用评级指标最优权重向量的确定方法，使信用评级体系的违约鉴别能力最大，属于信用服务技术领域。
背景技术
信用评级对当今经济社会有极其重要的影响。不论是主权信用评级、企业信用评级、银行信用评级，还是个人信用评级。若信用评级结果不合理，无法准确评估违约风险，必将误导投资者和社会公众。小到导致银行和企业的倒闭，大到引发金融危机、乃至整个经济社会的紊乱。一个合理的信用评级体系要有强的违约鉴别能力，能够将违约客户和非违约客户有效地区分开，准确地识别出违约风险大的客户。
对指标进行赋权、计算信用得分是信用评级中必不可少的重要环节。
信用评价方程是指标数据与权重向量的函数，故指标权重的大小、权重向量的结构与评级结果的好坏具有必然的联系。
不言而喻，对同一组指标赋予不同的权重，评价结果会大相径庭。因此，权重向量是否合理是决定评级结果能否准确地识别违约风险的关键要素。
现有的信用评级赋权研究可以分为以下三类：
一是基于专家判断的主观赋权。中华人民共和国知识产权局专利号为201710669426.X的“企业信用评级方法”和专利号为201410334653.3的“一种基于层次分析法的信用评价方法”利用AHP层次分析法，根据专家判断矩阵确定多层次评价指标的权重，计算企业信用分数。
二是基于计量统计、人工智能等方法的客观赋权。中华人民共和国知识产权局专利号为201710428343.1的“一种员工信用评价和应用的方法、装置及电子 设备”建立信用等级的逻辑回归模型，采用极大似然估计算法，计算每个指标对应的权重。中华人民共和国知识产权局专利号为201511031192.3的“一种基于深度学习的企业信用评价方法”利用深度学习的算法对指标权重进行调优，让认知和生成达到一致。美国专利商标局专利号为41118586的“Consumer behaviors at lender level”利用统计回归分析的方法对指标进行赋权，评价消费者的信用风险。世界知识产权组织专利号为WO/2014/121019的“Methods and systems for automatically generating high quality adverse action notifications”利用遗传算法进行赋权构建信用评价模型，识别贷款人的违约风险。
三是主客观组合赋权法。中华人民共和国知识产权局专利号为201611001902.2的“一种基于主客观赋权多模型组合验证的企业信用评价方法及系统”对指标采取主观和客观权重赋值相结合的方法进行企业信用评价，并进行Kendall一致性检验。
上述的主观赋权并不反映指标权重与违约状态的相互关系，更不反映评级结果与真实违约状态之间的相互关系。
上述的客观赋权虽然反映了指标权重与违约状态的相互关系，但并不反映评级结果与真实违约状态之间的相互关系。
事实上，信用评级是由客户的信用得分这个信用评级结果确定的，若割裂了权重向量与评级结果精度的内在联系，则怎样确定的权重都不是最优的。
本发明通过违约的差客户的评级结果逼近最低得分，非违约的好客户的得分逼近最高得分的逼近理想点的方法构建多目标规划函数，在信用得分的违约鉴别能力最大的极值条件下，反推一组信用评价方程的最优权重。确保信用评级结果、即信用评价方程得分的大小、能够显著区分违约与非违约客户。
发明内容
本发明的目的是提供一种使得信用评级结果的违约鉴别能力最大的最优权重向量的确定方法。
本发明的技术方案：
基于逼近理想点违约鉴别能力最大的信用评级最优权重向量的方法，将正理想点定义为各项指标的最大值加权后的得分，表示最高分；将负理想点定义为各项指标的最小值加权后的得分，表示最低分；
以非违约企业的信用得分到正理想点的欧式距离代数和最小，违约企业的信用得分到负理想点的欧式距离代数和最小为第一个目标函数；以“非违约企业得分与正理想点的距离”的离散程度最小、“违约企业得分与负理想点的距离”的离散程度最小为第二个目标函数，构建多目标规划函数，反推一组信用评价方程的最优权重，保证信用评价方程的评价结果为非违约企业得分最高、而违约企业得分最低，最大程度地减少两类样本之间的交叉重叠；
具体步骤如下：
步骤1：构建信用风险评价指标体系
首先通过偏相关分析，在海选指标中剔除反映信息重复的冗余指标；再通过Probit回归从上述筛选后保留的指标体系中，遴选出对违约状态有显著区分能力的指标，得到信用风险评价指标体系；
构建信用风险评价指标体系是后续赋权构建信用评价方程的基础，并且具有若干种确定方法；
步骤2：导入数据
将步骤1中有显著区分能力的指标数据、客户的违约状态(违约客户为1、非违约客户为0)导入到Excel文件中；将导入的指标数据进行标准化处理，转化 成[0,1]区间内的数据，消除量纲的影响；
步骤3：构建距离函数
步骤3.1、确定正负理想点：正理想点表示各项指标的最大值加权后的得分、即信用得分的最大值，由于各项指标数据标准化后的最大值为1，所以信用得分的最大值为1分，即正理想点S +＝1；
负理想点表示各项指标的最小值加权后的得分、即信用得分的最小值，由于各项指标数据标准化后的最小值为0，所以信用得分的最小值为0分，即负理想点S -＝0；
步骤3.2、构建距离函数：构建非违约企业信用得分
Figure PCTCN2018073568-appb-000001
到正理想点S +的距离函数
Figure PCTCN2018073568-appb-000002
其中，w j是指标权重、待求的决策变量，
Figure PCTCN2018073568-appb-000003
是步骤2中非违约企业的指标标准化数据，S +是步骤3.1确定的正理想点；
构建违约企业信用得分
Figure PCTCN2018073568-appb-000004
到负理想点S -的距离函数
Figure PCTCN2018073568-appb-000005
其中，
Figure PCTCN2018073568-appb-000006
是步骤2中违约企业的指标标准化数据，S -是步骤3.1确定的负理想点；
步骤4：第一个目标函数的构建
根据非违约企业的信用得分与正理想点的欧式距离
Figure PCTCN2018073568-appb-000007
代数和最小、违约企业的信用得分与负理想点的欧式距离
Figure PCTCN2018073568-appb-000008
代数和最小，构建目标函数1，即：
Figure PCTCN2018073568-appb-000009
其中，n 0是非违约企业的个数，C是罚系数，n 1是违约企业的个数；
在式(1)中引入“罚系数C”的原因是：第一个连加项
Figure PCTCN2018073568-appb-000010
的非违约企业数 n 0远大于第二个连加项
Figure PCTCN2018073568-appb-000011
的违约企业数n 1；第一个连加项由于数值较大，在目标函数1中所占的重要性要远大于第二个连加项，这样就造成了样本非平衡问题；
所以，通过罚系数C的引入，使得式(1)中第一项
Figure PCTCN2018073568-appb-000012
与第二项
Figure PCTCN2018073568-appb-000013
的重要程度之比变为n 0：C×n 1＝n 0：(n 0/n 1)×n 1＝1:1；使得式(1)中非违约和违约两类样本的连加距离可以同等程度地趋近于最小，解决了样本非平衡的问题；
以式(1)为第一个目标函数构建规划模型，反推一组信用评级方程的最优权重向量；保证信用评价方程的评价结果使得非违约企业的得分最高、违约企业的得分最低，通过信用得分能够显著区分违约与非违约客户；
步骤5：第二个目标函数的构建
通过“非违约企业得分到正理想点距离
Figure PCTCN2018073568-appb-000014
的离散程度最小、“违约企业得分到负理想点距离
Figure PCTCN2018073568-appb-000015
的离散程度最小构建第二个目标函数，即：
Figure PCTCN2018073568-appb-000016
其中，
Figure PCTCN2018073568-appb-000017
是非违约企业得分到正理想点距离
Figure PCTCN2018073568-appb-000018
的平均值，
Figure PCTCN2018073568-appb-000019
是违约企业得分到负理想点距离
Figure PCTCN2018073568-appb-000020
的平均值；
以式(2)为第二个目标函数构建规划模型，反推一组信用评级方程的最优权重向量；保证信用评价方程的评价结果使得违约企业和非违约企业得分在各自组内的离散程度最小，最大程度地减少两类样本之间的交叉重叠；
第一个目标函数与第二个目标函数的区别在于第一个目标函数是保证非违约企业得分最高、而违约企业得分最低，而第二个目标函数是使得违约企业和非违约企业得分的交叉重叠最小；
步骤6：约束条件的构建
以“全部指标的权重加和等于1，
Figure PCTCN2018073568-appb-000021
“指标权重非负w j≥0”为两个约束条件；
本方法中通过步骤4的第一个目标函数、步骤5的第二个目标函数和两个约束条件，构建多目标规划模型；反推信用评价方程的一组最优权重向量，使得信用评价结果满足非违约企业得分聚集在正理想点附近、且违约企业得分聚集在负理想点附近，最大地拉开两类企业的得分差距；
步骤7：求解最优的权重向量
将多目标规划模型中第一个目标函数式(1)与第二个目标函数式(2)，按照1：1的比例进行线性加权，得到单目标函数规划模型；而约束条件不变，利用单纯形法对单目标规划模型进行求解，得到决策变量“一组权重向量W *＝(w 1 *,w 2 *,…,w m *)”；权重的求解结果直接显示于Excel界面；
步骤8：计算信用评价得分
利用步骤4的权重求解结果w j *、步骤2的指标标准化数据x ij，线性加权构建信用评价方程，计算信用得分
Figure PCTCN2018073568-appb-000022
本发明的有益效果：
一是本发明提供了一种基于信用得分违约鉴别能力最大反推一组最优权重向量的方法。本发明的赋权方法能够保证评价方程的信用得分，满足非违约企业的信用得分最高、违约企业的信用得分最低，使得信用得分最大程度地区分开违约企业与非违约企业。
这一功能的实现是由于目标函数式(1)“逼近理想点”反推赋权的构建思路。满足目标函数式(1)的权重则必然能使非违约企业得分和违约企业得分两极化，前者最高、后者最低。
二是本发明的赋权方法能够保证评价方程的信用得分，满足非违约与违约两类企业的得分交叉重叠最小、混在一起的可能性最小，使得“违约判为非违约”、“非违约判为违约”的错判可能性降到最小。
这一功能的实现是由于目标函数式(2)“离散度最小”反推赋权的构建思路。满足目标函数式(2)的权重则必然能使非违约企业得分和违约企业得分在各自组内的离散程度最小，从而最大程度地避免违约和非违约企业得分混淆在一起。
三是利用本发明反推权重计算信用得分，更加合理地评价一笔贷款或债务的违约风险大小。可使得商业银行、债权人、社会公众等广大投资者，了解债券、贷款等债务的违约状况，进行投资决策。
四是本发明的赋权模型具有指标遴选的功能。当求解出的指标权重w j＝0时，说明该指标对于“区分开违约企业得分和非违约企业得分”是无作用的，可以删除，达到指标遴选的目标。
附图说明
图1是违约与非违约两类企业信用得分的示意图。
在图1中，实线圆圈代表非违约企业的信用得分区间，虚线圆圈代表违约企业的信用得分区间，中间部分是二者的交叉重叠区间。第一个目标函数式(1)的几何意义是使得图1中非违约企业所在的实线圆圈最接近右边的正理想点S +，违约企业所在的虚线圆圈最接近左边的负理想点S -。第二个目标函数式(2)的几何意义是使图1中间的交叠区域最小。
图2是基于逼近理想点违约鉴别能力最大的赋权原理。
具体实施方式
以下结合附图和技术方案，进一步说明本发明的具体实施方式。
本发明的目的是提供一种使得信用评级结果的违约鉴别能力最大的最优权 重确定方法。
本发明的目的通过以下技术方案来实现：
以非违约企业的信用得分到正理想点的欧式距离代数和最小、违约企业的信用得分到负理想点的欧式距离代数和最小为第一个目标函数。以“非违约企业得分与正理想点的距离”的离散程度最小、“违约企业得分与负理想点的距离”的离散程度最小为第二个目标函数，构建多目标规划函数，反推一组信用评价方程的最优权重。
以中国某地区性商业银行分布在京津沪渝等28个城市的1814笔工业小企业贷款数据为实证样本，对本发明所述方案进行实证分析。其中，非违约样本1799笔，违约样本数15笔。具体步骤如下：
步骤1：构建信用风险评价指标体系。
首先通过偏相关分析在海选指标中剔除反映信息重复的冗余指标。再通过Probit回归从上述筛选后保留的指标体系中，遴选出对违约状态有显著区分能力的指标，得到信用风险评价指标体系。
信用风险评价指标体系如表1第2列所示。
表1 信用风险评价指标体系及指标权重
(1)序号 (2)指标 (3)权重w j *
1 X 1资产负债率 0
2 X 2速动比率 0.1
… … …
14 X 14城市居民人均可支配收入 0.314
15 X 15相关行业从业年限 0.012
… … …
19 X 19年龄 0.098
20 X 20担任该职务时间 0.01
… … …
24 X 24抵质押担保得分 0.065
构建信用风险评价指标体系是后续赋权构建信用评价方程的基础，并且具 有若干种确定方法。
步骤2：导入数据。
将指标数据、客户的违约状态(违约客户为1、非违约客户为0)导入到Excel文件中。将导入的指标数据进行标准化处理，转化成[0,1]区间内的数据，消除量纲的影响。
步骤3：建立多目标规划模型。
步骤3.1：确定正负理想点。正理想点是信用得分的最大值，由于各项指标数据标准化后的最大值为1，所以信用得分的最大值为1分，即正理想点S +＝1。负理想点是信用得分的最小值，由于各项指标数据标准化后的最小值为0，所以信用得分的最小值为0分，即负理想点S -＝0。
步骤3.2：构建距离函数。将步骤2中非违约企业的指标标准化数据
Figure PCTCN2018073568-appb-000023
步骤3.1的正理想点S +＝1，代入公式
Figure PCTCN2018073568-appb-000024
得到非违约企业信用得分到正理想点的距离函数。
将步骤2中违约企业的指标标准化数据
Figure PCTCN2018073568-appb-000025
步骤3.1的负理想点S -＝0，代入公式
Figure PCTCN2018073568-appb-000026
得到违约企业信用得分到负理想点的距离函数。
步骤4：第一个目标函数的构建。
利用步骤3.2确定的“非违约企业得分与正理想点的欧式距离
Figure PCTCN2018073568-appb-000027
代数和最小、“违约企业的信用得分与负理想点的欧式距离
Figure PCTCN2018073568-appb-000028
代数和最小构建目标函数1，即
Figure PCTCN2018073568-appb-000029
其中，n 0是非违约企业的个数，n 1是违约企业的个数。C是为了解决样本非平衡问题引入的罚系数，且C＝n 0/n 1。
以目标函数1构建规划模型，反推一组信用评级方程的最优权重向量。保证信用评价方程的评价结果使得非违约企业的得分最高、违约企业的得分最低。其几何意义是使得图1中非违约企业所在的实线圆圈最接近右边的正理想点S +，违约企业所在的虚线圆圈最接近左边的负理想点S -。
步骤5：第二个目标函数的构建。
利用步骤3.2确定的“非违约企业得分到正理想点距离
Figure PCTCN2018073568-appb-000030
的离散程度最小、“违约企业得分到负理想点距离
Figure PCTCN2018073568-appb-000031
的离散程度最小构建目标函数2，即obj2：
Figure PCTCN2018073568-appb-000032
其中，
Figure PCTCN2018073568-appb-000033
是步骤3.2中确定的距离函数
Figure PCTCN2018073568-appb-000034
的平均值，
Figure PCTCN2018073568-appb-000035
是步骤3.2中确定的距离函数
Figure PCTCN2018073568-appb-000036
的平均值。
以目标函数2构建规划模型，反推一组信用评级方程的最优权重向量。保证信用评价方程的评价结果使得违约企业和非违约企业得分在各自组内的离散程度最小，最大程度地减少两类样本之间的交叉重叠。其几何意义是使图1中间的交叠区域最小。
目标函数1与目标函数2的区别在于目标函数1是保证非违约企业得分最高、而违约企业得分最低，而目标函数2是使得违约企业和非违约企业得分的交叉重叠最小。
步骤6：约束条件的构建。
以“全部指标的权重加和等于1，
Figure PCTCN2018073568-appb-000037
“指标权重非负w j≥0”为两个约束条件。
本专利通过步骤4的目标函数1、步骤5的目标函数2、步骤6的两个约束条件，构建多目标规划模型。反推信用评价方程的一组最优权重向量，确保信 用评级方程得分的大小、能够显著区分违约与否的客户。保证信用评级方程的评级结果为非违约企业得分最高、而违约企业得分最低，最大程度地减少两类样本之间的交叉重叠。原理如图2所示。
步骤7：求解最优的权重向量。
将多目标规划模型中第一个目标函数obj1与第二个目标函数obj2，按照1：1的比例进行线性加权，得到单目标函数。而约束条件不变，如步骤6所述。利用单纯形法对单目标规划模型进行求解，得到决策变量“一组权重向量W *＝(w 1 *,w 2 *,…,w m *)”。权重的求解结果直接显示于Excel界面。
权重向量的求解结果如表1第3列所示。
步骤8：计算信用评价得分。
利用表1第3列的权重求解结果w j *、步骤2的指标标准化数据x ij，线性加权构建信用评价方程，计算信用得分
Figure PCTCN2018073568-appb-000038
表2 权重的对比分析
Figure PCTCN2018073568-appb-000039
将本发明赋权方法与现有研究经典的赋权方法进行对比分析。表2中第3列是本发明得到的权重，第4列是基于变异系数法得到的权重，第5列是基于F统计量得到的权重。
对比分析的方法和标准：通过J-T非参数检验统计量，检验赋权后得到的信 用得分违约鉴别能力。J-T检验统计量越大，信用得分越能显著区分违约与非违约客户，权重向量的违约鉴别能力越大。
由表2最后一行可知，本发明建立的赋权模型的违约鉴别能力(Z＝6.526)大于现有研究的两种常用组合赋权模型、即基于变异系数的赋权(Z＝3.961)和基于F统计量的赋权(Z＝5.846)。说明本研究建立的赋权模型，在违约鉴别能力上要高于现有研究的传统赋权模型。
本发明尚有多种具体的实施方式，凡采用本发明所述“基于信用相似度最大的信用等级最优划分方法”等同替换、或者等效变换而形成的所有技术方案，均落在本发明要求保护的范围内。

Claims (1)

  1. 一种基于逼近理想点违约鉴别能力最大的信用评级最优权重向量的方法，其特征在于，步骤如下：
    步骤1：构建信用风险评价指标体系
    首先通过偏相关分析，在海选指标中剔除反映信息重复的冗余指标；再通过Probit回归从上述筛选后保留的指标体系中，遴选出对违约状态有显著区分能力的指标，得到信用风险评价指标体系；
    步骤2：导入数据
    将步骤1中有显著区分能力的指标数据、客户的违约状态导入到Excel文件中；将导入的指标数据进行标准化处理，转化成[0,1]区间内的数据，消除量纲的影响；其中，客户的违约状态分为违约客户为1和非违约客户为0；
    步骤3：构建距离函数
    步骤3.1、确定正负理想点：正理想点表示各项指标的最大值加权后的得分、即信用得分的最大值，由于各项指标数据标准化后的最大值为1，所以信用得分的最大值为1分，即正理想点S +＝1；
    负理想点表示各项指标的最小值加权后的得分、即信用得分的最小值，由于各项指标数据标准化后的最小值为0，所以信用得分的最小值为0分，即负理想点S -＝0；
    步骤3.2、构建距离函数：构建非违约企业信用得分
    Figure PCTCN2018073568-appb-100001
    到正理想点S +的距离函数
    Figure PCTCN2018073568-appb-100002
    其中，w j是指标权重、待求的决策变量，
    Figure PCTCN2018073568-appb-100003
    是步骤2中非违约企业的指标标准化数据，S +是步骤3.1确定的正理想点；
    构建违约企业信用得分
    Figure PCTCN2018073568-appb-100004
    到负理想点S -的距离函数
    Figure PCTCN2018073568-appb-100005
    其中，
    Figure PCTCN2018073568-appb-100006
    是步骤2中违约企业的指标标准化数 据，S -是步骤3.1确定的负理想点；
    步骤4：第一个目标函数的构建
    根据非违约企业的信用得分与正理想点的欧式距离
    Figure PCTCN2018073568-appb-100007
    代数和最小、违约企业的信用得分与负理想点的欧式距离
    Figure PCTCN2018073568-appb-100008
    代数和最小，构建目标函数1，即：
    Figure PCTCN2018073568-appb-100009
    其中，n 0是非违约企业的个数，C是罚系数，n 1是违约企业的个数；
    以式(1)为第一个目标函数构建规划模型，反推一组信用评级方程的最优权重向量；保证信用评价方程的评价结果使得非违约企业的得分最高、违约企业的得分最低，通过信用得分能够显著区分违约与非违约客户；
    步骤5：第二个目标函数的构建
    通过“非违约企业得分到正理想点距离
    Figure PCTCN2018073568-appb-100010
    ”的离散程度最小、“违约企业得分到负理想点距离
    Figure PCTCN2018073568-appb-100011
    ”的离散程度最小构建第二个目标函数，即：
    Figure PCTCN2018073568-appb-100012
    其中，
    Figure PCTCN2018073568-appb-100013
    是非违约企业得分到正理想点距离
    Figure PCTCN2018073568-appb-100014
    的平均值，
    Figure PCTCN2018073568-appb-100015
    是违约企业得分到负理想点距离
    Figure PCTCN2018073568-appb-100016
    的平均值；
    以式(2)为第二个目标函数构建规划模型，反推一组信用评级方程的最优权重向量；保证信用评价方程的评价结果使得违约企业和非违约企业得分在各自组内的离散程度最小，最大程度地减少两类样本之间的交叉重叠；
    第一个目标函数与第二个目标函数的区别在于第一个目标函数是保证非违约企业得分最高、而违约企业得分最低，而第二个目标函数是使得违约企业和非违约企业得分的交叉重叠最小；
    步骤6：约束条件的构建
    以“全部指标的权重加和等于1，
    Figure PCTCN2018073568-appb-100017
    ”、“指标权重非负w j≥0”为两个约束条件；
    本方法中通过步骤4的第一个目标函数、步骤5的第二个目标函数和两个约束条件，构建多目标规划模型；反推信用评价方程的一组最优权重向量，使得信用评价结果满足非违约企业得分聚集在正理想点附近、且违约企业得分聚集在负理想点附近，最大地拉开两类企业的得分差距；
    步骤7：求解最优的权重向量
    将多目标规划模型中第一个目标函数式(1)与第二个目标函数式(2)，按照1：1的比例进行线性加权，得到单目标函数规划模型；而约束条件不变，利用单纯形法对单目标规划模型进行求解，得到决策变量“一组权重向量W *＝(w 1 *,w 2 *,…,w m *)”；权重的求解结果直接显示于Excel界面；
    步骤8：计算信用评价得分
    利用步骤4的权重求解结果w j *、步骤2的指标标准化数据x ij，线性加权构建信用评价方程，计算信用得分
    Figure PCTCN2018073568-appb-100018
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