The Hitting Time Density for a Reflected Brownian Motion

Abstract

Reflected Brownian motion has been played an important role in economics, finance, queueing and many other fields. In this paper, we present the explicit spectral representation for the hitting time density of the reflected Brownian motion with two-sided barriers, and give some detailed analysis on the computational issues. Numerical analysis reveals that the spectral representation is more appealing than the method of numerical Laplace inversion. Two applications are included at the end of the paper.

Keywords: Reflected Brownian motion, hitting time, distribution function, density function, spectral representation, bankrupt probability, defaultable bond

JEL Classification: C63