IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v200y2012i1p131-14610.1007-s10479-011-0892-5.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-0892-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-011-0892-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Miklos Rasonyi, 2015. "Maximizing expected utility in the Arbitrage Pricing Model," Papers 1508.07761, arXiv.org, revised Mar 2017.
    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.
    3. Miklós Rásonyi, 2016. "On Optimal Strategies For Utility Maximizers In The Arbitrage Pricing Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-12, November.
    4. Chuong Luong & Nikolai Dokuchaev, 2016. "Modeling Dependency Of Volatility On Sampling Frequency Via Delay Equations," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-21, June.
    5. Francis Comets & Nobuo Yoshida, 2011. "Branching Random Walks in Space–Time Random Environment: Survival Probability, Global and Local Growth Rates," Journal of Theoretical Probability, Springer, vol. 24(3), pages 657-687, September.
    6. Michał Baran, 2007. "Asymptotic pricing in large financial markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(1), pages 1-20, August.
    7. Fan, Xiequan & Grama, Ion & Liu, Quansheng, 2012. "Hoeffding’s inequality for supermartingales," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3545-3559.
    8. Bas Peeters & Cees L. Dert & André Lucas, 2003. "Black Scholes for Portfolios of Options in Discrete Time: the Price is Right, the Hedge is wrong," Tinbergen Institute Discussion Papers 03-090/2, Tinbergen Institute.
    9. Kraft, Holger & Steffensen, Mogens, 2008. "How to invest optimally in corporate bonds: A reduced-form approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 348-385, February.
    10. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Post-Print hal-03898927, HAL.
    11. Laurence Carassus & Miklós Rásonyi, 2020. "From small markets to big markets," Post-Print hal-04833471, HAL.
    12. repec:dau:papers:123456789/12663 is not listed on IDEAS
    13. Christophe Cuny & Jérôme Dedecker & Florence Merlevède, 2024. "Strong Approximations for a Class of Dependent Random Variables with Semi-Exponential Tails," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2234-2252, September.
    14. Laurence Carassus & Miklos Rasonyi, 2019. "Risk-neutral pricing for APT," Papers 1904.11252, arXiv.org, revised Oct 2020.
    15. Fernando Cordero & Lavinia Perez-Ostafe, 2014. "Critical transaction costs and 1-step asymptotic arbitrage in fractional binary markets," Papers 1407.8068, arXiv.org.
    16. Nikolai Dokuchaev, 2015. "Optimal portfolio with unobservable market parameters and certainty equivalence principle," Papers 1502.02352, arXiv.org.
    17. Ben Hambly & Juozas Vaicenavicius, 2015. "The 3/2 Model As A Stochastic Volatility Approximation For A Large-Basket Price-Weighted Index," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-25.
    18. Paolo Guasoni & Constantinos Kardaras & Scott Robertson & Hao Xing, 2014. "Abstract, classic, and explicit turnpikes," Finance and Stochastics, Springer, vol. 18(1), pages 75-114, January.
    19. Soumik Pal, 2016. "Exponentially concave functions and high dimensional stochastic portfolio theory," Papers 1603.01865, arXiv.org, revised Mar 2016.
    20. Oleksii Mostovyi & Pietro Siorpaes, 2025. "Pricing of contingent claims in large markets," Finance and Stochastics, Springer, vol. 29(1), pages 177-217, January.
    21. Hong Ben Yee & Nikolai Dokuchaev, 2015. "Construction Of Models For Bounded Price Processes: The Case Of The Hkd Exchange Rate," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 1-23, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:200:y:2012:i:1:p:131-146:10.1007/s10479-011-0892-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.