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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_a
14-01-00739
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

Full text: PDF file (282 kB)
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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
Received in October 2014

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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\paper Two-sided disorder problem for a~Brownian motion in a~Bayesian setting
\inbook Stochastic calculus, martingales, and their applications
\bookinfo Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2014
\vol 287
\pages 211--233
\publ MAIK Nauka/Interperiodica
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