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Non-Arbitrage Under Additional Information for Thin Semimartingale Models

Author

Listed:
  • Anna Aksamit
  • Tahir Choulli
  • Jun Deng
  • Monique Jeanblanc

Abstract

This paper completes the two studies undertaken in \cite{aksamit/choulli/deng/jeanblanc2} and \cite{aksamit/choulli/deng/jeanblanc3}, where the authors quantify the impact of a random time on the No-Unbounded-Risk-with-Bounded-Profit concept (called NUPBR hereafter) when the stock price processes are quasi-left-continuous (do not jump on predictable stopping times). Herein, we focus on the NUPBR for semimartingales models that live on thin predictable sets only and the progressive enlargement with a random time. For this flow of information, we explain how far the NUPBR property is affected when one stops the model by an arbitrary random time or when one incorporates fully an honest time into the model. This also generalizes \cite{choulli/deng} to the case when the jump times are not ordered in anyway. Furthermore, for the current context, we show how to construct explicitly local martingale deflator under the bigger filtration from those of the smaller filtration.

Suggested Citation

  • Anna Aksamit & Tahir Choulli & Jun Deng & Monique Jeanblanc, 2015. "Non-Arbitrage Under Additional Information for Thin Semimartingale Models," Papers 1505.00997, arXiv.org.
    • Handle: RePEc:arx:papers:1505.00997
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    References listed on IDEAS

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    1. Kardaras, Constantinos, 2014. "On the characterisation of honest times that avoid all stopping times," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 373-384.
    2. Mark Loewenstein & Gregory A. Willard, 2000. "Local martingales, arbitrage, and viability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 135-161.
    3. Axel Grorud & Monique Pontier, 1998. "Insider Trading in a Continuous Time Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 331-347.
    4. 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.
    5. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    6. Arturo Kohatsu‐Higa & Agnès Sulem, 2006. "Utility Maximization In An Insider Influenced Market," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 153-179, January.
    7. Anna Aksamit & Tahir Choulli & Jun Deng & Monique Jeanblanc, 2013. "Non-Arbitrage up to Random Horizon for Semimartingale Models," Papers 1310.1142, arXiv.org, revised Feb 2014.
    8. Hardy Hulley & Martin Schweizer, 2010. "M6 - On Minimal Market Models and Minimal Martingale Measures," Research Paper Series 280, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Constantinos Kardaras, 2012. "Market viability via absence of arbitrage of the first kind," Finance and Stochastics, Springer, vol. 16(4), pages 651-667, October.
    10. Freddy Delbaen & Walter Schachermayer, 1998. "A Simple Counterexample to Several Problems in the Theory of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 1-11, January.
    11. Tahir Choulli & Christophe Stricker & Jia Li, 2007. "Minimal Hellinger martingale measures of order q," Finance and Stochastics, Springer, vol. 11(3), pages 399-427, July.
    12. Tahir Choulli & Anna Aksamit & Jun Deng & Monique Jeanblanc, 2014. "Non-Arbitrage under a Class of Honest Times," Papers 1404.0410, arXiv.org, revised Apr 2016.
    13. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    14. Kasper Larsen & Gordan v{Z}itkovi'c, 2011. "On utility maximization under convex portfolio constraints," Papers 1102.0346, arXiv.org, revised Feb 2013.
    15. 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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    Cited by:

    1. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio and num\'eraire portfolio for market models stopped at a random time," Papers 1810.12762, arXiv.org, revised Aug 2020.
    2. Tahir Choulli & Sina Yansori, 2018. "Explicit description of all deflators for market models under random horizon with applications to NFLVR," Papers 1803.10128, arXiv.org, revised Feb 2021.

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