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Two-sided disorder problem for a Brownian motion in a Bayesian setting

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Abstract

A two-sided disorder problem for a Brownian motion in a Bayesian setting is considered. It is shown how to reduce this problem to the standard optimal stopping problem for a posterior probability process. Qualitative properties of a solution are analyzed; namely, the concavity, continuity, and the smooth-fit principle for the risk function are proved. Optimal stopping boundaries are characterized as a unique solution to some integral equation.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    A. A. Muravlev & A. N. Shiryaev

  2. International Laboratory of Quantitative Finance, National Research University Higher School of Economics, ul. Shabolovka 31B, Moscow, 115162, Russia

    A. A. Muravlev

  3. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    A. N. Shiryaev

Authors
  1. A. A. Muravlev
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  2. A. N. Shiryaev
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Correspondence to A. A. Muravlev.

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Original Russian Text © A.A. Muravlev, A.N. Shiryaev, 2014, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Vol. 287, pp. 211–233.

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Muravlev, A.A., Shiryaev, A.N. Two-sided disorder problem for a Brownian motion in a Bayesian setting. Proc. Steklov Inst. Math. 287, 202–224 (2014). https://doi.org/10.1134/S0081543814080124

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  • DOI: https://doi.org/10.1134/S0081543814080124

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