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No-arbitrage up to random horizon for quasi-left-continuous models

Author

Listed:
  • Anna Aksamit

    (University of Oxford)

  • Tahir Choulli

    () (University of Alberta)

  • Jun Deng

    (University of International Business and Economics)

  • Monique Jeanblanc

    (Université d’Evry-Val-d’Essonne)

Abstract

Abstract This paper studies the impact, on no-arbitrage conditions, of stopping the price process at an arbitrary random time. As price processes, we consider the class of quasi-left-continuous semimartingales, i.e., semimartingales that do not jump at predictable stopping times. We focus on the condition of no unbounded profit with bounded risk (called NUPBR), also known in the literature as no arbitrage of the first kind. The first principal result describes all the pairs of quasi-left-continuous market models and random times for which the resulting stopped model fulfils NUPBR. Furthermore, for a subclass of quasi-left-continuous local martingales, we construct explicitly martingale deflators, i.e., strictly positive local martingales whose product with the price process stopped at a random time is a local martingale. The second principal result characterises the random times that preserve NUPBR under stopping for any quasi-left-continuous model. The analysis carried out in the paper is based on new stochastic developments in the theory of progressive enlargements of filtrations.

Suggested Citation

  • Anna Aksamit & Tahir Choulli & Jun Deng & Monique Jeanblanc, 2017. "No-arbitrage up to random horizon for quasi-left-continuous models," Finance and Stochastics, Springer, vol. 21(4), pages 1103-1139, October.
  • Handle: RePEc:spr:finsto:v:21:y:2017:i:4:d:10.1007_s00780-017-0337-3
    DOI: 10.1007/s00780-017-0337-3
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    References listed on IDEAS

    as
    1. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
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    3. 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.
    4. 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.
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    7. Koichiro Takaoka & Martin Schweizer, 2014. "A note on the condition of no unbounded profit with bounded risk," Finance and Stochastics, Springer, vol. 18(2), pages 393-405, April.
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    Citations

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    Cited by:

    1. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio without NFLVR: existence, complete characterization, and duality," Papers 1807.06449, arXiv.org.
    2. Tahir Choulli & Catherine Daveloose & Mich`ele Vanmaele, 2018. "Mortality/longevity Risk-Minimization with or without securitization," Papers 1805.11844, arXiv.org.
    3. repec:spr:finsto:v:22:y:2018:i:1:d:10.1007_s00780-017-0345-3 is not listed on IDEAS
    4. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio and num\'eraire portfolio under random horizon," Papers 1810.12762, arXiv.org.
    5. Tahir Choulli & Sina Yansori, 2018. "Explicit description of all deflators for markets under random horizon," Papers 1803.10128, arXiv.org, revised Oct 2018.

    More about this item

    Keywords

    No unbounded profit with bounded risk; No arbitrage; Random horizon; Informational arbitrage; Deflators; Quasi-left-continuous semimartingales; Progressive enlargement of filtration; Stochastic calculus;

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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