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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.

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  • 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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    References listed on IDEAS

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    10. Shiqi Song, 2013. "An alternative proof of a result of Takaoka," Papers 1306.1062, arXiv.org.
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    Cited by:

    1. Tahir Choulli & Jun Deng, 2014. "Non-arbitrage for Informational Discrete Time Market Models," Papers 1407.1453, arXiv.org.
    2. 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.
    3. Claudio Fontana, 2015. "The strong predictable representation property in initially enlarged filtrations under the density hypothesis," Papers 1508.03282, arXiv.org, revised Jun 2017.
    4. Karen Grigorian & Robert A. Jarrow, 2023. "Enlargement of Filtrations: An Exposition of Core Ideas with Financial Examples," Papers 2303.03573, arXiv.org.

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