Optimal stopping of a Brownian bridge with an unknown pinning point
Probability
2019-01-17 v3
Abstract
The problem of stopping a Brownian bridge with an unknown pinning point to maximise the expected value at the stopping time is studied. A few general properties, such as continuity and various bounds of the value function, are established. However, structural properties of the optimal stopping region are shown to crucially depend on the prior, and we provide a general condition for a one-sided stopping region. Moreover, a detailed analysis is conducted in the cases of the two-point and the mixed Gaussian priors, revealing a rich structure present in the problem.
Keywords
Cite
@article{arxiv.1705.00369,
title = {Optimal stopping of a Brownian bridge with an unknown pinning point},
author = {Erik Ekström and Juozas Vaicenavicius},
journal= {arXiv preprint arXiv:1705.00369},
year = {2019}
}
Comments
20 pages, 5 figures, small improvements in presentation