Optimally stopping a Brownian bridge with an unknown pinning time: A Bayesian approach

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:150

Article

Glover, Kristoffer¹ 

[1] Univ Technol Sydney, POB 123,Broadway, Sydney, NSW 2007, Australia

关键词: Optimal stopping;    Brownian bridges;    Random horizon;    Elastic killing;    Bang-bang Brownian motion;    Local time;   

DOI  :  10.1016/j.spa.2020.03.007

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free