Geodesic
The Absence of Arbitrage in a~Mixed Brownian--Fractional Brownian Model
Informatics and Automation, Stochastic financial mathematics, Tome 237 (2002), pp. 224-233

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A mixed version of the Black–Merton–Scholes model is considered, i.e. a market with a bond and a stock such that the stock is controlled by a linear combination of a Wiener process and a fractional Brownian motion. It is proved that such a market is arbitrage-free. As an auxiliary result, a representation of a fractional Brownian motion is obtained in terms of the “basic” Gaussian martingale with independent increments. 
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     author = {Yu. S. Mishura and E. Valkeila},
     title = {The {Absence} of {Arbitrage} in {a~Mixed} {Brownian--Fractional} {Brownian} {Model}},
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     year = {2002},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2002_237_a12/}
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Yu. S. Mishura; E. Valkeila. The Absence of Arbitrage in a~Mixed Brownian--Fractional Brownian Model. Informatics and Automation, Stochastic financial mathematics, Tome 237 (2002), pp. 224-233. http://geodesic.mathdoc.fr/item/TRSPY_2002_237_a12/