  We study a problem of finding an optimal stopping strategy to liquidate an
asset with unknown drift. Taking a Bayesian approach, we model the initial
beliefs of an individual about the drift parameter by allowing an arbitrary
probability distribution to characterise the uncertainty about the drift
parameter. Filtering theory is used to describe the evolution of the posterior
beliefs about the drift once the price process is being observed. An optimal
stopping time is determined as the first passage time of the posterior mean
below a monotone boundary, which can be characterised as the unique solution to
a non-linear integral equation. We also study monotonicity properties with
respect to the prior distribution and the asset volatility.
