Estimation of failure probability using semi-definite programming

Linear logit model is often used to predict the probability of bankruptcy. However, the failure probability need not depend on financial factors in a monotonic way. Also, we sometimes observe significant correlation among factors. In this paper, we propose three nonlinear logit models to remove drawbacks of the linear model mentioned above. First is the quadratic logit model which formulates the tendency of bankruptcy by a quadratic function. Second is the semi-definite programming (SDP) logit model which is constructed by limiting the quadratic function to a convex function, and the third is the NSDP logit model constructed by limiting the quadratic function to a concave function. The resulting SDP problems can be solved by using an efficient cutting plane algorithm. We show through simulations using real data that the SDP logit model performs better than linear and general quadratic logit model.