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On long-term arbitrage opportunities in Markovian models of financial markets

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  • Martin Mbele Bidima
  • Miklos Rasonyi

Abstract

A discrete-time infinite horizon stock market model is considered where the logarithm of the price is assumed to be a Markov chain arising from the time-discretization of a stochastic differential equation. Conditions are given which ensure that there exist investment strategies producing an exponential growth of wealth with a probability converging to 1. The rate of this convergence is studied using large deviation techniques. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Martin Mbele Bidima & Miklos Rasonyi, 2012. "On long-term arbitrage opportunities in Markovian models of financial markets," Annals of Operations Research, Springer, vol. 200(1), pages 131-146, November.
    • Handle: RePEc:spr:annopr:v:200:y:2012:i:1:p:131-146:10.1007/s10479-011-0892-5
    DOI: 10.1007/s10479-011-0892-5
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    References listed on IDEAS

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    1. Liu, Quansheng & Watbled, Frédérique, 2009. "Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3101-3132, October.
    2. Nikolai Dokuchaev, 2007. "Mean-Reverting Market Model: Speculative Opportunities and Non-Arbitrage," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 319-337.
    3. Y.M. Kabanov & D.O. Kramkov, 1998. "Asymptotic arbitrage in large financial markets," Finance and Stochastics, Springer, vol. 2(2), pages 143-172.
    4. Dmitry Rokhlin, 2008. "Asymptotic arbitrage and numéraire portfolios in large financial markets," Finance and Stochastics, Springer, vol. 12(2), pages 173-194, April.
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    Cited by:

    1. Martin Le Doux Mbele Bidima & Mikl'os R'asonyi, 2014. "Asymptotic Exponential Arbitrage and Utility-based Asymptotic Arbitrage in Markovian Models of Financial Markets," Papers 1406.5312, arXiv.org.
    2. Fatma Haba & Antoine Jacquier, 2015. "Asymptotic Arbitrage In The Heston Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-18, December.

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