Financial applications of the models with long-range dependence

In our work we move away from the semimartingale model of financial market and consider the models with so called long-range dependence. The arbitrage problems are discussed in the most general setting.
In particular, we consider financial market with risky asset governed by both the Wiener process and fractional Brownian motion with Hurst parameter $H>3/4$. Using Hitsuda and Cheridito representations for the mixed Brownian--fractional Brownian process, we present the solution of the problem of quantile hedging and clarify in
this case the dependence of maximal possible success probability on the available initial capital $\nu <H_0 $. More general problem of efficient hedging is also solved.