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The problem of stopping a Brownian bridge with an unknown pinning point tomaximise the expected value at the stopping time is studied. A few generalproperties, such as continuity and various bounds of the value function, areestablished. However, structural properties of the optimal stopping region areshown to crucially depend on the prior, and we provide a general condition fora one-sided stopping region. Moreover, a detailed analysis is conducted in thecases of the two-point and the mixed Gaussian priors, revealing a richstructure present in the problem.

Optimal stopping of a Brownian bridge with an unknown pinning point