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Teoriya Veroyatnostei i ee Primeneniya, 1997, Volume 42, Issue 3, Pages 564–575
DOI: https://doi.org/10.4213/tvp1953 (Mi tvp1953) 		 
This article is cited in 15 scientific papers (total in 15 papers)

On the Russian option: The expected waiting time

S. Graversen, G. Peskir

Institute of Mathematics, University of Aarhus, Denmark
Full-text PDF (529 kB) Citations (15)
DOI: https://doi.org/10.4213/tvp1953
Abstract: In the context of the Russian option of L. Shepp and A. N. Shiryaev, we present a new derivation of the solution for the underlying one-dimensional optimal stopping problem. Our method is not based on the smooth pasting guess and Ito formula, but only uses the strong Markov property. In addition, the exact formula is given for the expected waiting time of the optimal stopping strategy. Two different methods for this computation are presented. Both methods can be easily generalized to treat similar problems for general one-dimensional time-homogeneous diffusions.
Keywords: Russian option, infinitesimal operator, instantaneous reflection, the expected waitingtime, Cauchy type equation, Markov process, the strong Markov property, diffusion, Black–Scholes model, geometric Brownian motion, optimal stopping (strategy), payoff, the gainfunction, discounting, smooth pasting, Girsanov's change of measure.
Received: 05.03.1997
English version:
Theory of Probability and its Applications, 1998, Volume 42, Issue 3, Pages 416–425
DOI: https://doi.org/10.1137/S0040585X97976295
Bibliographic databases:
Language: English
Citation: S. Graversen, G. Peskir, “On the Russian option: The expected waiting time”, Teor. Veroyatnost. i Primenen., 42:3 (1997), 564–575; Theory Probab. Appl., 42:3 (1998), 416–425
Citation in format AMSBIB
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\by S.~Graversen, G.~Peskir
\paper On the Russian option: The expected waiting time
\jour Teor. Veroyatnost. i Primenen.
\yr 1997
\vol 42
\issue 3
\pages 564--575
\mathnet{http://mi.mathnet.ru/tvp1953}
\crossref{https://doi.org/10.4213/tvp1953}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1618803}
\zmath{https://zbmath.org/?q=an:0924.60012}
\transl
\jour Theory Probab. Appl.
\yr 1998
\vol 42
\issue 3
\pages 416--425
\crossref{https://doi.org/10.1137/S0040585X97976295}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000078491200004}
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  • https://www.mathnet.ru/eng/tvp1953
  • https://doi.org/10.4213/tvp1953
  • https://www.mathnet.ru/eng/tvp/v42/i3/p564
    • This publication is cited in the following 15 articles:
    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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