Stochastics and Finance Seminar: Kristoffer Glover -- Optimal stopping

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).