Optimal stopping of a Brownian bridge with an unknown pinning point

Erik Ekström, Juozas Vaicenavicius

Published 2017-04-30Version 1

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 of the value function are established. Structural properties of an optimal stopping region are shown to crucially depend on the prior. However, we provide a general condition for a one-sided stopping region. More detailed analysis is conducted in the cases of the two-point and the mixed Gaussian priors, revealing a rich structure present in the problem.