关键词: 违约判别, 最优指标组合, 利润, 最优权重, 支持向量机

Abstract: In recent years, the number of small enterprises in our country has continued to grow, and they have become the main force in economic development as well as an important force in creating new jobs and promoting innovation and entrepreneurship. However, due to the characteristics of small enterprises, such as incomplete financial information, high operating risks, less collateral, and low credit ratings, the problem of loan financing has long existed, which constrains the development of small enterprises. Solving the financing difficulties of small enterprises is of great significance for developing the national economy and promoting sustainable economic development. Taking into account the issue of the cost-benefit ratio, it is difficult for banks to accurately distinguish the default risk of small enterprises. How to establish a reasonable default discriminant model to help alleviate the current situation of small enterprises’ financing difficulties has become an urgent problem to be solved. Establishing a reasonable default discriminant model is of great significance to commercial credit and credit decisions between financial institutions including banks and enterprises.
In the domain of credit risk, because the dataset of enterprises is high-dimensional and characterized by redundant and irrelevant features, selecting the optimal feature subset helps reduce both the dimensionality of data and computation costs, and enhance the predictive capability of the classifier. Therefore, the determination of the optimal feature subset that identifies the default status of enterprises effectively is worth considering. This paper selects the optimal feature set collecting data of enterprises from internal financial factors, non-financial factors, and external macro factors. Firstly, Bootstrap samples are generated by sampling multiple instances from training data. In each subsample, we select the features that contribute to the default discriminant by computing feature importance scores measured by information gain using extreme gradient boosting (XGBoost), then candidate feature subsets are generated by calculating the intersection of selected features in each subsample, and finally, we select the optimal feature subset by using support vector machine (SVM) with an objective to maximize AUC.
Weight is a key factor affecting the accuracy of the default discriminant model, and reasonable weight has received widespread attention. In the process of building the model, weight reflects the importance of features. Different weights are assigned to the same features, and the results are different, or even completely opposite. How to determine the weights of features is the crucial problem to be discussed in this article. This paper adapts the idea of being profit-driven to the task of determining the weight vector of the feature. The profit is composed of the benefits associated to the correctly classified non-default enterprises minus the losses with respect to the misclassified non-default enterprises. An objective function is established by constructing the function relationship between the discriminant result of SVM and the profit obtained by distinguishing two groups of enterprises. A nonlinear programming model that maximizes the above-mentioned objective function is established to find the optimal penalty coefficient, and then the SVM model is built using the optimal penalty coefficient to find the optimal weight vector.
This article uses the credit data of small enterprises from a regional commercial bank as the research sample to validate the effectiveness of the proposed model. The empirical study shows that the optimal feature set covers the principle of credit evaluation 5C. Meanwhile, the profit and comprehensive precision of the proposed default discriminant model in the study are higher than those of the other six models, such as logistic regression, etc. Furthermore, the findings in this study illustrate that non-financial features of enterprises have the greatest impact on default discriminant with the weight of 0.475. Per capita disposable income of urban residents is the most important indicator that affects default discriminant with the weight of 0.12. This study provides a reference for the credit decisions of commercial banks and new insights into credit risk assessment for small enterprises.
The data of small enterprises is characterized by a highly imbalanced distribution of class between default samples (minority class) and non-default samples (majority class). In an imbalanced classification, the minority samples are usually ignored or misclassified. Future directions can consider a suitable sampling technique so as to improve the identification rate of default enterprises and thus boost the profit maximization effect.

Key words: default discriminant, optimal feature set, profit, optimal weight, support vector machine