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 Tr. Mat. Inst. Steklova, 2014, Volume 287, Pages 211–233 (Mi tm3591)

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

A. A. Muravlevab, A. N. Shiryaevca

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b International Laboratory of Quantitative Finance, National Research University Higher School of Economics, Moscow, Russia
c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia

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.

 Funding Agency Grant Number Russian Science Foundation 14-21-00162 Russian Foundation for Basic Research 14-01-31468-mol_a14-01-00739 The work was supported by the Russian Science Foundation, project no. 14-21-00162 (Sections 1-3), and by the Russian Foundation for Basic Research, project nos. 14-01-31468-mol_a and 14-01-00739 (Sections 4, 5).

DOI: https://doi.org/10.1134/S0371968514040128

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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 287:1, 202–224

Bibliographic databases:

Document Type: Article
UDC: 519.244

Citation: A. A. Muravlev, A. N. Shiryaev, “Two-sided disorder problem for a Brownian motion in a Bayesian setting”, Stochastic calculus, martingales, and their applications, Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 287, MAIK Nauka/Interperiodica, Moscow, 2014, 211–233; Proc. Steklov Inst. Math., 287:1 (2014), 202–224

Citation in format AMSBIB
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