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Mean-Reverting Market Model: Speculative Opportunities and Non-Arbitrage

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  • Nikolai Dokuchaev

Abstract

The paper studies arbitrage opportunities and possible speculative opportunities for diffusion mean-reverting market models. It is shown that the Novikov condition is satisfied for any time interval and for any set of parameters. It is non-trivial because the appreciation rate has Gaussian distribution converging to a stationary limit. It follows that the mean-reverting model is arbitrage-free for any finite time interval. Further, it is shown that this model still allows some speculative opportunities: a gain for a wide enough set of expected utilities can be achieved for a strategy that does not require any hypothesis on market parameters and does not use estimation of these parameters.

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  • Nikolai Dokuchaev, 2007. "Mean-Reverting Market Model: Speculative Opportunities and Non-Arbitrage," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 319-337.
    • Handle: RePEc:taf:apmtfi:v:14:y:2007:i:4:p:319-337
    DOI: 10.1080/13504860701255078
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. Nikolai Dokuchaev, 2015. "Optimal portfolio with unobservable market parameters and certainty equivalence principle," Papers 1502.02352, arXiv.org.
    4. 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.
    5. 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.

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