Title: First passage time distribution of jump-diffusion processes and nonlinear boundaries
Authors: Zhiyong Jin - University of Manitoba (Canada) [presenting]
Liqun Wang - University of Manitoba (Canada)
Abstract: First passage time (FPT) model of jump-diffusion processes is a very useful tool in finance and insurance, neuroscience and other scientific disciplines. The calculation of the FPT distribution for diffusion processes is a long-standing and notoriously difficult problem. While it is well-known that explicit formulas exist only for some special processes and boundaries, the problem is even more challenging for processes with jumps. We derive new formulas for piecewise linear boundary crossing probabilities and first passage time densities of Brownian motion with random jumps where the jump process can be any integer-valued counting process and jump sizes can be correlated and non-identically distributed. These formulas can be used to approximate the first passage time distributions for general nonlinear boundaries. The method can be extended to more general diffusion processes such as geometric Brownian motion and Ornstein-Uhlenbeck processes with jumps. The numerical computation is done through Monte Carlo integration which is straightforward and easy to implement. Some numerical examples are presented.