| In this paper, we are trying to find the distribution of the first hitting time for Brownian motion in particular, and for diffusion process in general. For the cases where the barrier is a horizontal line or a line with positive slope, the distributions are known. For general moving barrier, the distributions are not known. In those cases, approximation is needed. We then apply those results into mathematical finance context. An interesting stock price model where volatility is modeled as a stochastic process is considered. |
