Geodesic
Two-sided disorder problem for a Brownian motion in a Bayesian setting
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 211-233
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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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A. A. Muravlev; A. N. Shiryaev. Two-sided disorder problem for a Brownian motion in a Bayesian setting. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 211-233. http://geodesic.mathdoc.fr/item/TM_2014_287_a11/

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