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The existence of dominating local martingale measures

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  • Peter Imkeller
  • Nicolas Perkowski

Abstract

We prove that for locally bounded processes the absence of arbitrage opportunities of the first kind is equivalent to the existence of a dominating local martingale measure. This is related to and motivated by results from the theory of filtration enlargements. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Peter Imkeller & Nicolas Perkowski, 2015. "The existence of dominating local martingale measures," Finance and Stochastics, Springer, vol. 19(4), pages 685-717, October.
    • Handle: RePEc:spr:finsto:v:19:y:2015:i:4:p:685-717
    DOI: 10.1007/s00780-015-0264-0
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Miklós Rásonyi & Andrea Meireles‐Rodrigues, 2021. "On utility maximization under model uncertainty in discrete‐time markets," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 149-175, January.
    2. Andrew L. Allan & Christa Cuchiero & Chong Liu & David J. Prömel, 2023. "Model‐free portfolio theory: A rough path approach," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 709-765, July.
    3. Andrew L. Allan & Christa Cuchiero & Chong Liu & David J. Promel, 2021. "Model-free Portfolio Theory: A Rough Path Approach," Papers 2109.01843, arXiv.org, revised Oct 2022.
    4. Mathias Beiglböck & Alexander M. G. Cox & Martin Huesmann & Nicolas Perkowski & David J. Prömel, 2017. "Pathwise superreplication via Vovk’s outer measure," Finance and Stochastics, Springer, vol. 21(4), pages 1141-1166, October.
    5. David Criens, 2016. "Deterministic Criteria for the Absence and Existence of Arbitrage in Multi-Dimensional Diffusion Markets," Papers 1609.01621, arXiv.org, revised Dec 2017.
    6. David Criens, 2018. "Deterministic Criteria For The Absence And Existence Of Arbitrage In Multi-Dimensional Diffusion Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-41, February.
    7. Mathias Beiglbock & Alexander M. G. Cox & Martin Huesmann & Nicolas Perkowski & David J. Promel, 2015. "Pathwise super-replication via Vovk's outer measure," Papers 1504.03644, arXiv.org, revised Jul 2016.
    8. Acciaio, Beatrice & Fontana, Claudio & Kardaras, Constantinos, 2016. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1761-1784.
    9. Eckhard Platen & Stefan Tappe, 2020. "No arbitrage and multiplicative special semimartingales," Papers 2005.05575, arXiv.org, revised Sep 2022.
    10. 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.
    11. 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.
    12. Mikl'os R'asonyi & Andrea Meireles-Rodrigues, 2018. "On Utility Maximisation Under Model Uncertainty in Discrete-Time Markets," Papers 1801.06860, arXiv.org, revised Jul 2020.
    13. Thomas Krabichler & Josef Teichmann, 2020. "A constraint-based notion of illiquidity," Papers 2004.12394, arXiv.org.

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    More about this item

    Keywords

    Dominating local martingale measure; Arbitrage of the first kind; Fundamental theorem of asset pricing; Supermartingale densities; Föllmer’s measure; Enlargement of filtration; Jacod’s criterion; 60G44; 60G48; 91B70; 46N10; G10;
    All these keywords.

    JEL classification:

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

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