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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. Igor Evstigneev & Dhruv Kapoor, . "Arbitrage in Stationary Markets," Swiss Finance Institute Research Paper Series 07-32, Swiss Finance Institute.
    2. Miklós Rásonyi, 2004. "Arbitrage pricing theory and risk-neutral measures," Decisions in Economics and Finance, Springer, vol. 27(2), pages 109-123, December.
    3. 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, revised Jun 2013.
    4. 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.
    5. 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.
    6. 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 Jun 2013.
    7. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742 Elsevier.
    8. Mikl\'os R\'asonyi & Jos\'e G. Rodr\'iguez-Villarreal, 2014. "Optimal investment under behavioural criteria -- a dual approach," Papers 1405.3812, arXiv.org, revised Jun 2014.
    9. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and Duality in Nondominated Discrete-Time Models," Papers 1305.6008, arXiv.org, revised Feb 2014.
    10. Paolo Guasoni & Mikl\'os R\'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    11. Pierre Henry-Labordere & Nizar Touzi, 2013. "An Explicit Martingale Version of Brenier's Theorem," Working Papers hal-00790001, HAL.
    12. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2014. "Robust Arbitrage under Uncertainty in Discrete Time," Papers 1407.0948, arXiv.org.
    13. Ivan Guo & Marek Rutkowski, 2014. "Arbitrage Pricing of Multi-person Game Contingent Claims," Papers 1405.2718, arXiv.org.
    14. Pierre Henry-Labordere & Nizar Touzi, 2013. "An Explicit Martingale Version of Brenier's Theorem," Papers 1302.4854, arXiv.org, revised Apr 2013.
    15. 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.
    16. 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.
    17. 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.
    18. Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
    19. 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.
    20. Irle, A., 2004. "A measure-theoretic approach to completeness of financial markets," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 1-7, June.
    21. Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org, revised Feb 2014.
    22. 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.
    23. Miklos Rasonyi & Lukasz Stettner, 2005. "On utility maximization in discrete-time financial market models," Papers math/0505243, arXiv.org.

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