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A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing

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  • Christa Cuchiero
  • Josef Teichmann

Abstract

We show that no unbounded profit with bounded risk (NUPBR) implies predictable uniform tightness (P-UT), a boundedness property in the Emery topology introduced by Stricker (Séminaire de Probabilités de Strasbourg XIX, pp. 209–217, 1985 ). Combining this insight with well-known results of Mémin and Słominski (Séminaire de Probabilités de Strasbourg XXV, pp. 162–177, 1991 ) leads to a short variant of the proof of the fundamental theorem of asset pricing initially proved by Delbaen and Schachermayer (Math. Ann. 300:463–520, 1994 ). The results are formulated in the general setting of admissible portfolio wealth processes as laid down by Kabanov (Statistics and Control of Stochastic Processes, pp. 191–203, World Sci. Publ., River Edge, 1997 ). Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Christa Cuchiero & Josef Teichmann, 2015. "A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing," Finance and Stochastics, Springer, vol. 19(4), pages 743-761, October.
    • Handle: RePEc:spr:finsto:v:19:y:2015:i:4:p:743-761
    DOI: 10.1007/s00780-015-0276-9
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    References listed on IDEAS

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    1. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
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    3. Kardaras, Constantinos, 2013. "On the closure in the Emery topology of semimartingale wealth-process sets," LSE Research Online Documents on Economics 44996, London School of Economics and Political Science, LSE Library.
    4. W. Schachermayer, 1994. "Martingale Measures For Discrete‐Time Processes With Infinite Horizon," Mathematical Finance, Wiley Blackwell, vol. 4(1), pages 25-55, January.
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    Cited by:

    1. Christoph Kuhn, 2023. "The fundamental theorem of asset pricing with and without transaction costs," Papers 2307.00571, arXiv.org.
    2. Yuri Kabanov & Constantinos Kardaras & Shiqi Song, 2016. "No arbitrage of the first kind and local martingale numéraires," Finance and Stochastics, Springer, vol. 20(4), pages 1097-1108, October.
    3. Eckhard Platen & Stefan Tappe, 2020. "No arbitrage and multiplicative special semimartingales," Papers 2005.05575, arXiv.org, revised Sep 2022.
    4. Eckhard Platen & Stefan Tappe, 2020. "The Fundamental Theorem of Asset Pricing for Self-Financing Portfolios," Research Paper Series 411, Quantitative Finance Research Centre, University of Technology, Sydney.

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    More about this item

    Keywords

    Fundamental theorem of asset pricing; Emery topology; (NUPBR) condition; (P-UT) property; 60G48; 91B70; 91G99; G10;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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