Increasing accuracy of the model prediction on business bankruptcy helps reduce substantial losses for owners, creditors, investors and workers, and, further, minimize an economic and social problem frequently. In this study, we propose a stochastic model of financial working capital and cashflow as a two-dimensional Brownian motion X(t) = (X1(t),X2(t)) on the business bankruptcy prediction. The probability of bankruptcy occurring in a time interval [0,T] is defined by the boundary crossing probability of the two-dimensional Brownian motion entering a predetermined threshold domain. Mathematically, we extend the result in Fu and Wu (2016) on the boundary crossing probability of a high dimensional Brownian motion to an unbounded convex hull. The proposed model is applied to a real data set of companies in US and the numerical results show the proposed method performs well.
Brownian Motion and the Dirichlet Problem at Infinity on Two-dimensional Cartan-Hadamard Manifolds
