Credit Cards Scoring with Quadratic Utility Function

The paper considers a general approach for classifying objects using mathematical programming algorithms. The approach is based on optimizing a utility function, which is quadratic in indicator parameters and is linear in control parameters (which need to be identified). Qualitative characteristics of the utility function, such as monotonicity in some variables, are included using additional constraints. The methodology was tested with a "credit cards scoring" problem. Credit scoring is a way of separating specific subgroups in a population of objects (such as applications for credit), which have significantly different credit risk characteristics. A new feature of our approach is incorporating expert judgments in the model. For instance, the following preference was included with an additional constraint: “give more preference to customers with higher incomes.” Numerical experiments showed that including constraints based on expert judgments improves the performance of the algorithm. Introduction. In this paper, we consider a general approach for classifying objects and explain it with credit cards scoring problem. Classification can be defined by a classification function assigning to each object some categorical value called the class number. However, this classification function has a very inconvenient property – it is discontinuous (impossible to use it for classifying new objects). We reduce the classification problem to evaluating a continuous utility function from some general class of functions. This function is used for separating objects 1 University of Florida, ISE, Risk Management and Financial Engineering Lab, PO Box 116595, 303 Weil Hall, Gainesville, FL 32611-6595. E-mail: [email protected] 2 Chuo University, Dept. of Industrial and Systems Engineering, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan 3 University of Florida, ISE, Risk Management and Financial Engineering Lab, PO Box 116595, 303 Weil Hall, Gainesville, FL 32611-6595. E-mail: [email protected].