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Arbitrage of the first kind and filtration enlargements in semimartingale financial models

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  • Beatrice Acciaio
  • Claudio Fontana
  • Constantinos Kardaras

Abstract

In a general semimartingale financial model, we study the stability of the No Arbitrage of the First Kind (NA1) (or, equivalently, No Unbounded Profit with Bounded Risk) condition under initial and under progressive filtration enlargements. In both cases, we provide a simple and general condition which is sufficient to ensure this stability for any fixed semimartingale model. Furthermore, we give a characterisation of the NA1 stability for all semimartingale models.

Suggested Citation

  • 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.
  • Handle: RePEc:arx:papers:1401.7198
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    File URL: http://arxiv.org/pdf/1401.7198
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    References listed on IDEAS

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    1. repec:wsi:ijtafx:v:01:y:1998:i:03:n:s0219024998000199 is not listed on IDEAS
    2. Xin Guo & Yan Zeng, 2008. "Intensity process and compensator: A new filtration expansion approach and the Jeulin--Yor theorem," Papers 0801.3191, arXiv.org.
    3. Delia Coculescu & Monique Jeanblanc & Ashkan Nikeghbali, 2012. "Default times, no-arbitrage conditions and changes of probability measures," Finance and Stochastics, Springer, vol. 16(3), pages 513-535, July.
    4. repec:wsi:ijtafx:v:04:y:2001:i:02:n:s0219024901000961 is not listed on IDEAS
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    Cited by:

    1. Shiqi Song, 2014. "Local martingale deflators for asset processes stopped at a default time $S^\tau$ or right before $S^{\tau-}$," Papers 1405.4474, arXiv.org, revised Jul 2016.
    2. Tahir Choulli & Jun Deng, 2014. "Non-arbitrage for Informational Discrete Time Market Models," Papers 1407.1453, arXiv.org.

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