Credit cards scoring with quadratic utility functions

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.