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No-arbitrage under additional information for thin semimartingale models

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  • Aksamit, Anna
  • Choulli, Tahir
  • Deng, Jun
  • Jeanblanc, Monique

Abstract

This paper completes the studies undertaken in Aksamit et al. (2017, 2018) [[1,2]] and Choulli and Deng (2017) [[8]], where we quantify the impact of a random time on the no-unbounded-profit-with-bounded-risk concept (called NUPBR hereafter) for quasi-left-continuous models and discrete-time market models respectively. Herein, we focus on NUPBR for semimartingale models that live on thin predictable sets only and when the extra information about the random time is added progressively over time. This leads to the probabilistic setting of two filtrations where one filtration contains the other and makes the random time a stopping time. For this framework, we explain how far NUPBR is affected when one stops the model by an arbitrary random time, or when one incorporates in a progressive way an honest time into the model. Furthermore, we show how to construct explicitly some local martingale deflators in the largest filtration for a particular class of models. As a consequence, by combining the current results on the thin case and those of Aksamit et al. (2017, 2018) [[1,2]], we elaborate universal results for general semimartingale models.

Suggested Citation

  • Aksamit, Anna & Choulli, Tahir & Deng, Jun & Jeanblanc, Monique, 2019. "No-arbitrage under additional information for thin semimartingale models," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3080-3115.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:9:p:3080-3115
    DOI: 10.1016/j.spa.2018.09.005
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    References listed on IDEAS

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    Cited by:

    1. Ferdoos Alharbi & Tahir Choulli, 2022. "Log-optimal portfolio after a random time: Existence, description and sensitivity analysis," Papers 2204.03798, arXiv.org.
    2. Tahir Choulli & Catherine Daveloose & Michèle Vanmaele, 2020. "A martingale representation theorem and valuation of defaultable securities," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1527-1564, October.
    3. Tahir Choulli & Sina Yansori, 2022. "Log-optimal and numéraire portfolios for market models stopped at a random time," Finance and Stochastics, Springer, vol. 26(3), pages 535-585, July.
    4. Choulli, Tahir & Yansori, Sina, 2022. "Explicit description of all deflators for market models under random horizon with applications to NFLVR," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 230-264.
    5. H'el`ene Halconruy, 2021. "The insider problem in the trinomial model: a discrete-time jump process approach," Papers 2106.15208, arXiv.org, revised Sep 2023.

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