Failure discrimination by semi-definite programming

This paper addresses itself to a new approach for failure discriminant analysis, a classical and yet very actively studied problem in financial engineering. The basic idea of the new method is to separate multi-dimensional financial data corresponding to ongoing and failed enterprises by an ellipsoidal surface which enjoys a good mathematical property as well as a clear financial interpretation. We will apply a new cutting plane algorithm for solving a resulting semi-definite programming problem and show that it can generate an optimal solution in a much more efficient way than standard interior point algorithms. Computational results using financial data of Japanese enterprises show that the ellipsoidal separation leads to significantly better results than the hyperplane separation. Also it performs better than the separation by a general quadratic surface, a well used method in support vector machine approach.