Can anyone point me to the expression for the first passage time for a geometric Brownian motion process X(t) as a function of the starting point, threshold, drift and diffusion parameters.
I am mainly interested for processes with positive drift and thresholds that are higher than the starting point.
I know this is a standard expression, however all results I have found so far are specific to a particular starting point (e.g. X(0) = 0) and/or threshold of 1, and I am not sure how to generalize to any initial state and threshold value.
Any help would be much appreciated