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Local martingales and the fundamental asset pricing theorems in the discrete-time case

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Author Info

  • J. Jacod

    (Laboratoire de ProbabilitÊs, UniversitÊ P. et M. Curie et CNRS, URA 224, 4 Place Jussieu, F-75252-Paris Cedex, France)

  • A.N. Shiryaev

    (Steklov Mathematical Institute, Gubkina St. 8, Moscow, 117966 Russia Manuscript)

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    Abstract

    This paper is devoted to giving simpler proofs of the two fundamental theorems of asset pricing theory, in iscrete-time and finite horizon: namely the no-arbitrage theorem, and the market completeness theorem. Some elementary but apparently new results are also given on discrete-time martingale theory, and in particular a new condition for a local martingale to be a martingale.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 2 (1998)
    Issue (Month): 3 ()
    Pages: 259-273

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    Handle: RePEc:spr:finsto:v:2:y:1998:i:3:p:259-273

    Note: received: October 1996; final version received: December 1997
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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Arbitrage; complete models; equivalent martingale measure.;

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    Cited by:
    1. Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler & Rodrigo Rodriguez, 2012. "Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices," Papers 1205.4790, arXiv.org, revised Nov 2012.
    2. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
    3. Pierre Henry-Labordere & Nizar Touzi, 2013. "An Explicit Martingale Version of Brenier's Theorem," Working Papers hal-00790001, HAL.
    4. Miklós Rásonyi, 2004. "Arbitrage pricing theory and risk-neutral measures," Decisions in Economics and Finance, Springer, vol. 27(2), pages 109-123, December.
    5. Ralf Korn & Frank Oertel & Manfred Schäl, 2003. "Notes and Comments: The numeraire portfolio in financial markets modeled by a multi-dimensional jump diffusion process," Decisions in Economics and Finance, Springer, vol. 26(2), pages 153-166, November.
    6. Miklos Rasonyi & Lukasz Stettner, 2005. "On utility maximization in discrete-time financial market models," Papers math/0505243, arXiv.org.
    7. Balbas, Alejandro & Miras, Miguel Angel & Munoz-Bouzo, Maria Jose, 2002. "Projective system approach to the martingale characterization of the absence of arbitrage," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 311-323, July.
    8. Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
    9. Pierre Henry-Labordere & Nizar Touzi, 2013. "An Explicit Martingale Version of Brenier's Theorem," Papers 1302.4854, arXiv.org, revised Apr 2013.
    10. Tomasz R. Bielecki & Igor Cialenco & Rodrigo Rodriguez, 2012. "No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs," Papers 1205.6254, arXiv.org.
    11. Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org.
    12. Paolo Guasoni & Mikl\'os R\'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    13. Irle, A., 2004. "A measure-theoretic approach to completeness of financial markets," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 1-7, June.
    14. Igor Evstigneev & Dhruv Kapoor, . "Arbitrage in Stationary Markets," Swiss Finance Institute Research Paper Series 07-32, Swiss Finance Institute.
    15. Balbás, Alejandro & Balbás, Raquel & Mayoral, Silvia, 2007. "Risk-neutral valuation with infinitely many trading dates," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/13981, Universidad Carlos III de Madrid.
    16. Balbás, Alejandro & Downarowicz, Anna, 2007. "Infinitely many securities and the fundamental theorem of asset pricing," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/12972, Universidad Carlos III de Madrid.
    17. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "Pricing options on scenario trees," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 283-298, February.
    18. Alejandro Balbás & Miguel Ángel Mirás & María José Muñoz-Bouzo, 2001. "Projective System Approach To The Martingale Characterization Of The Absence Of Arbitrage," Business Economics Working Papers wb011505, Universidad Carlos III, Departamento de Economía de la Empresa.
    19. Alejandro Balbas & Anna Downarowicz, 2004. "Infinitely many securities and the fundamental theorem of asset pricing," Business Economics Working Papers wb043513, Universidad Carlos III, Departamento de Economía de la Empresa.
    20. Yuri Kabanov, 2008. "In discrete time a local martingale is a martingale under an equivalent probability measure," Finance and Stochastics, Springer, vol. 12(3), pages 293-297, July.

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