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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 \emph{No unbounded profit with bounded risk} (NUPBR) implies \emph{predictable uniform tightness} (P-UT), a boundedness property in the Emery topology which has been introduced by C. Stricker \cite{S:85}. Combining this insight with well known results from J. M\'emin and L. S{\l}ominski \cite{MS:91} leads to a short variant of the proof of the fundamental theorem of asset pricing initially proved by F. Delbaen and W. Schachermayer \cite{DS:94}. The results are formulated in the general setting of admissible portfolio wealth processes as laid down by Y. Kabanov in \cite{kab:97}.

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  • Christa Cuchiero & Josef Teichmann, 2014. "A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing," Papers 1406.5414, arXiv.org, revised Jul 2014.
    • Handle: RePEc:arx:papers:1406.5414
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    References listed on IDEAS

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    1. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    2. Freddy Delbaen, 1992. "Representing Martingale Measures When Asset Prices Are Continuous And Bounded," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 107-130, April.
    3. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Post-Print hal-03898927, HAL.
    2. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Finance and Stochastics, Springer, vol. 24(2), pages 465-511, April.
    3. Likuan Qin & Vadim Linetsky, 2014. "Long Term Risk: A Martingale Approach," Papers 1411.3078, arXiv.org, revised Oct 2016.
    4. Christa Cuchiero & Irene Klein & Josef Teichmann, 2014. "A new perspective on the fundamental theorem of asset pricing for large financial markets," Papers 1412.7562, arXiv.org, revised Oct 2023.
    5. Claudio Fontana & Zorana Grbac & Sandrine Gumbel & Thorsten Schmidt, 2018. "Term structure modeling for multiple curves with stochastic discontinuities," Papers 1810.09882, arXiv.org, revised Dec 2019.

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