Optimal stopping of a Brownian bridge with an unknown pinning point

Erik Ekström and Juozas Vaicenavicius

Stochastic Processes and their Applications, 2020, vol. 130, issue 2, 806-823

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: Brownian bridge; Optimal stopping; Sequential analysis; Stochastic filtering; Incomplete information (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.spa.2019.03.018

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