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Non-arbitrage for Informational Discrete Time Market Models

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  • Tahir Choulli
  • Jun Deng

Abstract

This paper focuses on the stability of the non-arbitrage condition in discrete time market models when some unknown information $\tau$ is partially/fully incorporated into the market. Our main conclusions are twofold. On the one hand, for a fixed market $S$, we prove that the non-arbitrage condition is preserved under a mild condition. On the other hand, we give the necessary and sufficient equivalent conditions on the unknown information $\tau$ to ensure the validity of the non-arbitrage condition for any market. Two concrete examples are presented to illustrate the importance of these conditions, where we calculate explicitly the arbitrage opportunities when they exist.

Suggested Citation

  • Tahir Choulli & Jun Deng, 2014. "Non-arbitrage for Informational Discrete Time Market Models," Papers 1407.1453, arXiv.org.
    • Handle: RePEc:arx:papers:1407.1453
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Schachermayer, W., 1992. "A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 249-257, December.
    4. 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.
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