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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, 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.

Suggested Citation

  • Peter Imkeller & Nicolas Perkowski, 2011. "The Existence of Dominating Local Martingale Measures," Papers 1111.3885, arXiv.org, revised Mar 2013.
    • Handle: RePEc:arx:papers:1111.3885
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    File URL: http://arxiv.org/pdf/1111.3885
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    References listed on IDEAS

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    1. Pal, Soumik & Protter, Philip, 2010. "Analysis of continuous strict local martingales via h-transforms," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1424-1443, August.
    2. Robert A. Jarrow, 2015. "Asset Price Bubbles," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 201-218, December.
    3. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 263-286, July.
    4. Soumik Pal & Philip Protter, 2007. "Analysis of continuous strict local martingales via h-transforms," Papers 0711.1136, arXiv.org, revised Jun 2010.
    5. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," SFB 373 Discussion Papers 1998,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Citations

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    Cited by:

    1. Neda Esmaeeli & Peter Imkeller, 2015. "American Options with Asymmetric Information and Reflected BSDE," Papers 1505.05046, arXiv.org, revised Aug 2017.
    2. Johannes Ruf & Wolfgang Runggaldier, 2013. "A Systematic Approach to Constructing Market Models With Arbitrage," Papers 1309.1988, arXiv.org, revised Dec 2013.
    3. Acciaio, Beatrice & Fontana, Claudio & Kardaras, Constantinos, 2016. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," LSE Research Online Documents on Economics 65150, London School of Economics and Political Science, LSE Library.
    4. repec:hum:wpaper:sfb649dp2013-021 is not listed on IDEAS
    5. Karen Grigorian & Robert A. Jarrow, 2023. "Enlargement of Filtrations: An Exposition of Core Ideas with Financial Examples," Papers 2303.03573, arXiv.org.
    6. Bibinger, Markus & Winkelmann, Lars, 2013. "Econometrics of co-jumps in high-frequency data with noise," SFB 649 Discussion Papers 2013-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Bibinger, Markus & Winkelmann, Lars, 2015. "Econometrics of co-jumps in high-frequency data with noise," Journal of Econometrics, Elsevier, vol. 184(2), pages 361-378.
    8. Beatrice Acciaio & Claudio Fontana & Constantinos Kardaras, 2014. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," Papers 1401.7198, arXiv.org, revised May 2015.

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