Dear Colleagues, You are cordially invited to the Stochastics and Finance Seminar at 2PM, Tuesday, August 20. The seminar will be held in AGR. Speaker: Kristoffer Glover Title: Optimally Stopping a Brownian Bridge with an Unknown Pinning Time: A Bayesian Approach Abstract: We consider the problem of optimally stopping a Brownian bridge with an unknown pinning time so as to maximise the value of the process upon stopping. Adopting a Bayesian approach, we allow the stopper to update their belief about the value of the pinning time through sequential observations of the process. Uncertainty in the pinning time influences both the conditional dynamics of the process and the expected (random) horizon of the optimal stopping problem. Structural properties of the optimal stopping region are shown to be qualitatively different under different prior distributions, however we provide a sufficient condition for the existence of a one-sided stopping region. Certain gamma and beta distributed priors are shown to satisfy this condition and these cases are subsequently considered in detail. A two-point prior distribution is also considered in which a richer structure emerges (with multiple optimal stopping boundaries).