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On the no-arbitrage market and continuity in the Hurst parameter

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  • Nikolai Dokuchaev

Abstract

We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we found that this approach eliminates the discontinuity of the stochastic integrals with respect to the Hurst parameter H at H=1/2.

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  • Nikolai Dokuchaev, 2015. "On the no-arbitrage market and continuity in the Hurst parameter," Papers 1509.06472, arXiv.org, revised Oct 2015.
    • Handle: RePEc:arx:papers:1509.06472
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    References listed on IDEAS

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    1. Es-Sebaiy, Khalifa & Ouassou, Idir & Ouknine, Youssef, 2009. "Estimation of the drift of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1647-1653, July.
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    3. Paolo Guasoni, 2006. "No Arbitrage Under Transaction Costs, With Fractional Brownian Motion And Beyond," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 569-582, July.
    4. Tomas Björk & Henrik Hult, 2005. "A note on Wick products and the fractional Black-Scholes model," Finance and Stochastics, Springer, vol. 9(2), pages 197-209, April.
    5. Christian Bender & Tommi Sottinen & Esko Valkeila, 2010. "Fractional processes as models in stochastic finance," Papers 1004.3106, arXiv.org.
    6. Salopek, D. M., 1998. "Tolerance to arbitrage," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 217-230, August.
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