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Optimal stopping of a Brownian bridge with an unknown pinning point

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  • Ekström, Erik
  • Vaicenavicius, Juozas

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.

Suggested Citation

  • Ekström, Erik & Vaicenavicius, Juozas, 2020. "Optimal stopping of a Brownian bridge with an unknown pinning point," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 806-823.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:806-823
    DOI: 10.1016/j.spa.2019.03.018
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    References listed on IDEAS

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    1. Marc Jeannin & Giulia Iori & David Samuel, 2008. "Modeling stock pinning," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 823-831.
    2. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    3. Umut c{C}etin & Albina Danilova, 2014. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," Papers 1407.2420, arXiv.org, revised Sep 2016.
    4. Marco Avellaneda & Michael Lipkin, 2003. "A market-induced mechanism for stock pinning," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 417-425.
    5. Çetin, Umut & Danilova, Albina, 2016. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," LSE Research Online Documents on Economics 63259, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. D'Auria, Bernardo & Guada Azze, Abel, 2021. "Optimal stopping of an Ornstein-Uhlenbeck bridge," DES - Working Papers. Statistics and Econometrics. WS 33508, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Glover, Kristoffer, 2022. "Optimally stopping a Brownian bridge with an unknown pinning time: A Bayesian approach," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 919-937.
    3. Maria B. Chiarolla & Tiziano Angelis & Gabriele Stabile, 2022. "An analytical study of participating policies with minimum rate guarantee and surrender option," Finance and Stochastics, Springer, vol. 26(2), pages 173-216, April.
    4. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal stopping of Gauss-Markov bridges," Papers 2211.05835, arXiv.org, revised Jul 2024.
    5. Bernardo D’Auria & Eduardo García-Portugués & Abel Guada, 2020. "Discounted Optimal Stopping of a Brownian Bridge, with Application to American Options under Pinning," Mathematics, MDPI, vol. 8(7), pages 1-27, July.

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