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Teor. Veroyatnost. i Primenen., 1994, Volume 39, Issue 3, Pages 635–640 (Mi tvp3839)  

This article is cited in 5 scientific papers (total in 5 papers)

Short Communications

No-arbitrage and equivalent martingale measures: an elementary proof of the Harrison–Pliska theorem

Yu. M. Kabanova, D. O. Kramkovb

a Central Economics and Mathematics Institute, RAS
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We give a new proof of a key result to the theorem that in the discrete-time stochastic model of a frictionless security market the absence of arbitrage possibilities is equivalent to the existence of a probability measure $Q$ which is absolute continuous with respect to the basic probability measure $P$ with the strictly positive and bounded density and such that all security prices are martingales with respect to $Q$. The proof is elementary in a sense that it does not involve a measurable selection theorem.

Keywords: security market, no-arbitrage, equivalent martingale measure.

Full text: PDF file (402 kB)

English version:
Theory of Probability and its Applications, 1994, 39:3, 523–527

Bibliographic databases:

Received: 02.07.1993

Citation: Yu. M. Kabanov, D. O. Kramkov, “No-arbitrage and equivalent martingale measures: an elementary proof of the Harrison–Pliska theorem”, Teor. Veroyatnost. i Primenen., 39:3 (1994), 635–640; Theory Probab. Appl., 39:3 (1994), 523–527

Citation in format AMSBIB
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\by Yu.~M.~Kabanov, D.~O.~Kramkov
\paper No-arbitrage and equivalent martingale measures: an elementary proof of the Harrison--Pliska theorem
\jour Teor. Veroyatnost. i Primenen.
\yr 1994
\vol 39
\issue 3
\pages 635--640
\mathnet{http://mi.mathnet.ru/tvp3839}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1347191}
\zmath{https://zbmath.org/?q=an:0834.60045}
\transl
\jour Theory Probab. Appl.
\yr 1994
\vol 39
\issue 3
\pages 523--527
\crossref{https://doi.org/10.1137/1139038}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TF06800013}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Shiryaev, A. S. Cherny, “Vector Stochastic Integrals and the Fundamental Theorems of Asset Pricing”, Proc. Steklov Inst. Math., 237 (2002), 6–49  mathnet  mathscinet  zmath
    2. D. B. Rokhlin, “An extended version of the Dalang–Morton–Willinger theorem under portfolio constraints”, Theory Probab. Appl., 49:3 (2005), 429–443  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Schachermayer W., “The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time”, Mathematical Finance, 14:1 (2004), 19–48  crossref  mathscinet  zmath  isi
    4. A. S. Cherny, “Pricing with coherent risk”, Theory Probab. Appl., 52:3 (2008), 389–415  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Klein I., Lepinette E., Perez-Ostafe L., “Asymptotic Arbitrage With Small Transaction Costs”, Financ. Stoch., 18:4 (2014), 917–939  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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