2019/02/26 by Kristoffer Glover, Glover, Kristoffer · 2 citations
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #62F15 #62L15 #Applications (stat.AP) #Auction Theory and Applications #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Search Problems #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR #msc:62F15 #msc:62L15 #stat.AP
paper · pdf · doi:10.48550/arxiv.1902.10261
20 pages, 3 figures
openalex publication_date 2019/02/26 · arxiv created 2020/03/14 · arxiv updated 2020/03/17 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
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 assume the stopper has a general continuous prior and is allowed 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. We analyse certain gamma and beta distributed priors in detail. Remarkably, the optimal stopping problem in the gamma case becomes time homogeneous and is completely solvable in closed form. Moreover, in the beta case we find that the optimal stopping boundary takes on a square-root form, similar to the classical solution with a known pinning time.