Can anyone provide the expression and source for the running maximum $M_t$ for geometric Brownian motion $X_t$ as a function of the initial value $X_0$, drift $\mu$ and diffusion $\sigma$? $X_t$ evolves as
$X_t = X_0*exp[(\mu-\sigma^2/2)t + \sigma W_t] $
where $W_t$ is a Wiener process
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