Optimal stopping of a Brownian bridge with an unknown pinning point |
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| Institution: | 1. Department of Physics, McGill University, 3600 University Street, Montreal, Quebec, H3A2T8, Canada;2. Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA;3. Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata 700064, India;1. Fachbereich Mathematik, Technische Universität Kaiserslautern, Erwin-Schrödinger Straße, 67653 Kaiserslautern, Germany;2. Fachgruppe Stochastik am Mathematischen Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Straße 4, 24098 Kiel, Germany;3. Department of Mathematics, SPST, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany;4. School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland;1. University of Kragujevac, Faculty of Science, R. Domanovića 12, 34000 Kragujevac, Serbia;2. University of Belgrade, Faculty of Physics, POB 44, 11001 Belgrade, Serbia;1. School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China;2. College of Science, Civil Aviation University of China, Tianjin 300300, PR China |
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| 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. |
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| Keywords: | Brownian bridge Optimal stopping Sequential analysis Stochastic filtering Incomplete information |
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