On arbitrage and replication in the fractional Black-Scholes pricing model

摘要

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-Ito-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.