Linear and Non-Linear Boundary Crossing Probabilities for Brownian Motion and Their Applications to Predicting the Bankruptcy of Manufacture Companies
James C. Fu
Department of Statistics, University of Manitoba, Winnipeg, Manitoba, Canada

Recently a new method to obtain the boundary crossing probabilities for linear or non-linear boundaries for Brownian motion was proposed by Fu and Wu (JAP 2010). The method also covers certain classes of stochastic processes associated with Brownian motion. The method is based on finite Markov Chain imbedding technique. The main aim of this manuscript is to applying the method for predicting bankruptcy of manufacture companies. Examples are given to illustrate the method. The numerical results show that the proposed method performs better than methods such as logistic regression and multivariate discriminant analysis.

Keywords: Linear and non-linear boundaries; Finite Markov chain imbedding; Brownian motion; Bankruptcy

Biography: Dr. Fu is an emeritus professor of University of Manitoba. He is also a fellow of IMS and has been associate edditors for several statistics journals. His main research areas are large sample estimation, statistics foundation, finite Markov chain imbedding technique, distribution theory of runs and patterns, and applied probability.