  We consider optimal stopping problems for a Brownian motion and a geometric
Brownian motion with a "disorder", assuming that the moment of a disorder is
uniformly distributed on a finite interval. Optimal stopping rules are found as
the first hitting times of some Markov process (the Shiryaev-Roberts statistic)
to time-dependent boundaries, which are characterized by certain Volterra
integral equations. The problems considered are related to mathematical finance
and can be applied in questions of choosing the optimal time to sell an asset
with changing trend.
