In this paper an arbitrage strategy is constructed for the modified Black–Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the heavy tailedness of the log returns of the stock...

This paper extends a recent martingale representation result of [N-S] for a Levy process to filtrations generated by a rather large class of semimartingales. As in [N-S], we assume the underlying processes have moments of all orders, but here we allow angle brackets to be stochastic. Following...

In this paper it is shown that the space of stochastic integrals w.r. to a special semimartingal is closed and hence every square integrable random variable admits a best approximation in this space. In terms of financial economics this means that for every contingent claim there exists a...