Estimation of failure probability using semi-definite logit model

We will propose a new and practical method for estimating the failure probability of a large number of small to medium scale companies using their balance sheet data. We will use the maximum likelihood method to estimate the best parameters of the logit function, where the failure intensity function in its exponent is represented as a convex quadratic function instead of a commonly used linear function. The reasons for using this type of function are: (i) it can better represent the observed nonlinear dependence of failure probability on financial attributes, (ii) the resulting likelihood function can be maximized using a cutting plane algorithm developed for nonlinear semi-definite programming problems. We will show that we can achieve better prediction performance than the standard logit model, using thousands of sample companies.