  The problem of stopping a Brownian bridge with an unknown pinning point to
maximise the expected value at the stopping time is studied. A few general
properties, such as continuity and various bounds of the value function, are
established. However, structural properties of the optimal stopping region are
shown to crucially depend on the prior, and we provide a general condition for
a one-sided stopping region. Moreover, a detailed analysis is conducted in the
cases of the two-point and the mixed Gaussian priors, revealing a rich
structure present in the problem.
