Survival Analysis Employed in Predicting Corporate Failure: A Forecasting Model Proposal

In face of the current economic and financial environment, predicting corporate bankruptcy is arguably a phenomenon of increasing interest to investors, creditors, borrowing firms, and governments alike. Within the strand of literature focused on bankruptcy forecasting we can find diverse types of research employing a wide variety of techniques, but only a few researchers have used survival analysis for the examination of this issue. We propose a model for the prediction of corporate bankruptcy based on survival analysis, a technique which stands on its own merits. In this research, the hazard rate is the probability of ‘‘bankruptcy’’ as of time t, conditional upon having survived until time t. Many hazard models are applied in a context where the running of time naturally affects the hazard rate. The model employed in this paper uses the time of survival or the hazard risk as dependent variable, considering the unsuccessful companies as censured observations.

Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.