Characteristics of the Fractional Brownian Market:Arbitrage and Its Exclusion

In this chapter we investigate the characteristics of the fractional Brownian market when it is based on the continuous stochastic process. In particular, we discuss in Sect. 4.1 thoroughly the problem of arbitrage. Furthermore we will present in Sect. 4.2 the diverse approaches that have been stressed during the last few years to overcome the existence of arbitrage. We then focus on the problem of dynamical completion showing regard to the specific character of fractional Brownian motion. As a result, Sect. 4.4 will show that the renouncement of continuous tradability combined with the transition to a preference-based pricing poses a passable way to give a sensible meaning to the problem of asset pricing in fractional Brownian markets.