  In this study, it is theoretically proven that the expected value of maximum
loss of fractional Brownian motion (fBm) up to time 1 with Hurst parameter
$[1/2,1)$ is bounded above by $2/\sqrt{\pi}$ and below by $1/\sqrt{\pi}$. This
result is generalized for fBm with $H\in[1/2,1)$ up to any fixed time, $t$.
This also leads us to the bounds related to the distribution of maximum loss of
fBm. As numerical study some lower bounds on the expected value of maximum loss
of fBm up to time 1 are obtained by discretization. Simulation study is
conducted with Cholesky method. Finally, comparison of the established bounds
with simulation results is given.
