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Teor. Veroyatnost. i Primenen., 2013, Volume 58, Issue 1, Pages 193–200 (Mi tvp4500)  

Short Communications

Optimal stopping problems for a Brownian motion with disorder on a segment

M. V. Zhitlukhinab, A. N. Shiryaeva

a Steklov Mathematical Institute of the Russian Academy of Sciences
b University of Manchester

Abstract: We consider optimal stopping problems for a Brownian motion and a geometric Brownian motion with “disorder”, assuming that the moment of disorder is uniformly distributed on a finite segment. The optimal stopping rules are found as the times of first hitting of the time-dependent boundaries which are characterized by certain integral equations by some Markov process (the Shiryaev–Roberts statistic). The problems considered are related to mathematical finance and can be applied in questions of choosing the optimal time to sell an asset with the changing trend.

Keywords: optimal stopping problems; disorder detection problems; Shiryaev–Roberts statistic.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0073
Russian Foundation for Basic Research 11-01-00949-a
12-01-31449-мол а


DOI: https://doi.org/10.4213/tvp4500

Full text: PDF file (162 kB)
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English version:
Theory of Probability and its Applications, 2014, 58:1, 164–171

Bibliographic databases:

Document Type: Article
MSC: 60G40,60J65,91G80
Received: 13.12.2012

Citation: M. V. Zhitlukhin, A. N. Shiryaev, “Optimal stopping problems for a Brownian motion with disorder on a segment”, Teor. Veroyatnost. i Primenen., 58:1 (2013), 193–200; Theory Probab. Appl., 58:1 (2014), 164–171

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