Abstract
This paper focuses on the first exit time for a Brownian motion with a double linear time-dependent barrier specified by y=a+bt, y=ct, (a>0, b<0, c>0). We are concerned in this paper with the distribution of the Brownian motion hitting the upper barrier before hitting the lower linear barrier. The main method we applied here is the Girsanov transform formula. As a result, we expressed the density of such exit time in terms of a finite series. This result principally provides us an analytical expression for the distribution of the aforementioned exit time and an easy way to compute the distribution of first exit time numerically.
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