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Article: Optimal selling time in stock market over a finite time horizon

TitleOptimal selling time in stock market over a finite time horizon
Authors
KeywordsBuy and hold
Local time
Optimal stopping
Stock selling
Issue Date2012
PublisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/10255/
Citation
Acta Mathematicae Applicatae Sinica, 2012, v. 28 n. 3, p. 557-570 How to Cite?
AbstractIn this paper, we examine the best time to sell a stock at a price being as close as possible to its highest price over a finite time horizon [0, T], where the stock price is modelled by a geometric Brownian motion and the 'closeness' is measured by the relative error of the stock price to its highest price over [0, T]. More precisely, we want to optimize the expression: where (V t) t≥0 is a geometric Brownian motion with constant drift α and constant volatility σ > 0, is the running maximum of the stock price, and the supremum is taken over all possible stopping times 0 ≤ τ ≤ T adapted to the natural filtration (F t) t≥0 of the stock price. The above problem has been considered by Shiryaev, Xu and Zhou (2008) and Du Toit and Peskir (2009). In this paper we provide an independent proof that when α=1/2σ 2 a selling strategy is optimal if and only if it sells the stock either at the terminal time T or at the moment when the stock price hits its maximum price so far. Besides, when α>1/2σ 2, selling the stock at the terminal time T is the unique optimal selling strategy. Our approach to the problem is purely probabilistic and has been inspired by relating the notion of dominant stopping ρ τ of a stopping time τ to the optimal stopping strategy arisen in the classical 'Secretary Problem'. © 2012 Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.
Persistent Identifierhttp://hdl.handle.net/10722/156287
ISSN
2015 Impact Factor: 0.25
2015 SCImago Journal Rankings: 0.220
ISI Accession Number ID
Funding AgencyGrant Number
Hong Kong RGC GRF502909
Hong Kong Polytechnic UniversityAPC0D
G-YH96
University of Hong Kong201109176016
Funding Information:

The first author was supported by the Hong Kong RGC GRF 502909, The Hong Kong Polytechnic University Internal Grant APC0D, and The Hong Kong Polytechnic University Collaborative Research Grant G-YH96. The second author was supported by an internal grant of code 201109176016 from the University of Hong Kong.

References

 

DC FieldValueLanguage
dc.contributor.authorYam, SCPen_US
dc.contributor.authorYung, SPen_US
dc.contributor.authorZhou, Wen_US
dc.date.accessioned2012-08-08T08:41:11Z-
dc.date.available2012-08-08T08:41:11Z-
dc.date.issued2012en_US
dc.identifier.citationActa Mathematicae Applicatae Sinica, 2012, v. 28 n. 3, p. 557-570en_US
dc.identifier.issn0168-9673en_US
dc.identifier.urihttp://hdl.handle.net/10722/156287-
dc.description.abstractIn this paper, we examine the best time to sell a stock at a price being as close as possible to its highest price over a finite time horizon [0, T], where the stock price is modelled by a geometric Brownian motion and the 'closeness' is measured by the relative error of the stock price to its highest price over [0, T]. More precisely, we want to optimize the expression: where (V t) t≥0 is a geometric Brownian motion with constant drift α and constant volatility σ > 0, is the running maximum of the stock price, and the supremum is taken over all possible stopping times 0 ≤ τ ≤ T adapted to the natural filtration (F t) t≥0 of the stock price. The above problem has been considered by Shiryaev, Xu and Zhou (2008) and Du Toit and Peskir (2009). In this paper we provide an independent proof that when α=1/2σ 2 a selling strategy is optimal if and only if it sells the stock either at the terminal time T or at the moment when the stock price hits its maximum price so far. Besides, when α>1/2σ 2, selling the stock at the terminal time T is the unique optimal selling strategy. Our approach to the problem is purely probabilistic and has been inspired by relating the notion of dominant stopping ρ τ of a stopping time τ to the optimal stopping strategy arisen in the classical 'Secretary Problem'. © 2012 Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.en_US
dc.languageengen_US
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/10255/en_US
dc.relation.ispartofActa Mathematicae Applicatae Sinicaen_US
dc.rightsThe original publication is available at www.springerlink.com-
dc.subjectBuy and holden_US
dc.subjectLocal timeen_US
dc.subjectOptimal stoppingen_US
dc.subjectStock sellingen_US
dc.titleOptimal selling time in stock market over a finite time horizonen_US
dc.typeArticleen_US
dc.identifier.emailYung, SP: spyung@hku.hken_US
dc.identifier.authorityYung, SP=rp00838en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1007/s10255-012-0169-zen_US
dc.identifier.scopuseid_2-s2.0-84862255896en_US
dc.identifier.hkuros209523-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84862255896&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume28en_US
dc.identifier.issue3en_US
dc.identifier.spage557en_US
dc.identifier.epage570en_US
dc.identifier.isiWOS:000305126700011-
dc.publisher.placeGermanyen_US
dc.identifier.scopusauthoridZhou, W=55251981000en_US
dc.identifier.scopusauthoridYung, SP=7006540951en_US
dc.identifier.scopusauthoridYam, SCP=35112610600en_US
dc.identifier.citeulike10797199-

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