The Absence of Arbitrage in a Mixed Brownian–Fractional Brownian Model

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.