On Arbitrage and Replication in the Fractional Black Scholes Pricing Model

It has been proposed that the arbitrage possibility in the fractional Black–Scholes model depends on the definition of the stochastic integral. More precisely, if one uses the Wick– Itô–Skorohod integral one obtains an arbitrage-free model. However, this integral does not allow economical interpretation. On the other hand it is easy to give arbitrage examples in continuous time trading with self-financing strategies, if one uses the Riemann-Stieltjes integral. In this note we discuss the connection between two different notions of self-financing portfolios in the fractional Black–Scholes model by applying the known connection between these two integrals. In particular, we give an economical interpretation of the proposed arbitrage-free model in terms of Riemann– Stieltjes integrals.