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Teoriya Veroyatnostei i ee Primeneniya, 2013, Volume 58, Issue 1, Pages 193–200
DOI: https://doi.org/10.4213/tvp4500 (Mi tvp4500) 		 
This article is cited in 4 scientific papers (total in 4 papers)

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
Full-text PDF (162 kB) Citations (4)
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DOI: https://doi.org/10.4213/tvp4500
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
Received: 13.12.2012
English version:
Theory of Probability and its Applications, 2014, Volume 58, Issue 1, Pages 164–171
DOI: https://doi.org/10.1137/S0040585X97986448
Bibliographic databases:
Document Type: Article
MSC: 60G40,60J65,91G80
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    1. Cagin Uru, Savas Dayanik, Semih O. Sezer, “Compound Poisson disorder problem with uniformly distributed disorder time”, Bernoulli, 29:3 (2023)  crossref
    2. G. I. Belyavskii, N. V. Danilova, “Upravlenie v binarnykh modelyakh s razladkoi”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 15:3 (2022), 67–82  mathnet  crossref
    3. Xu Z.Q. Yi F., “Optimal Redeeming Strategy of Stock Loans Under Drift Uncertainty”, Math. Oper. Res., 45:1 (2020), 384–401  crossref  mathscinet  zmath  isi
    4. Albert N. Shiryaev, Probability Theory and Stochastic Modelling, 93, Stochastic Disorder Problems, 2019, 239  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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