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On the law of one price

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Abstract.

We consider the standard discrete-time model of a frictionless financial market and show that the law of one price holds if and only if there exists a martingale density process with strictly positive initial value. In contrast to the classical no-arbitrage criteria, this density process may change its sign. We also give an application to the CAPM.

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Authors and Affiliations

  1. L.I.B.R.E., Université de Franche-Comté, Avenue de l’Observatoire, 25030, Besançon Cedex, France

    Jean-Michel Courtault

  2. Department für Mathematik,, Eidgenössische Technische Hochschule Zürich, ETH-Zentrum, 8092, Zürich, Schweiz

    Freddy Delbaen

  3. Université de Franche-Comté, 16 Route de Gray, 25030, Besançon Cedex, France

    Yuri Kabanov

  4. Central Economics and Mathematics Institute, Moscow, Russia

    Yuri Kabanov

  5. Université de Franche-Comté, 16 Route de Gray, 25030, Besançon Cedex, France

    Christophe Stricker

Authors
  1. Jean-Michel Courtault
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  2. Freddy Delbaen
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  3. Yuri Kabanov
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  4. Christophe Stricker
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Corresponding author

Correspondence to Jean-Michel Courtault.

Additional information

Received: November 2003,

Mathematics Subject Classification (2000):

60G44

JEL Classification:

G13, G11

Freddy Delbaen: This research was done during the stay of the author at Université de Franche-Comté.

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Courtault, JM., Delbaen, F., Kabanov, Y. et al. On the law of one price. Finance and Stochastics 8, 525–530 (2004). https://doi.org/10.1007/s00780-004-0124-9

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  • DOI: https://doi.org/10.1007/s00780-004-0124-9

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