The generalization of the quantile hedging problem for price process model involving finite number of Brownian and fractional Brownian motions

The paper is devoted to the problem of quantile hedging of contingent claims in the framework of a model defined by the finite number of independent Brownian and fractional Brownian motions. The maximal success probability depending on initial capital is estimated

Fractional Processes as Models in Stochastic Finance

Abstract. We survey some new progress on the pricing models driven by fractional Brownian motion or mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We summarize some recent results on fractional Black & Scholes pricing model with transaction costs. We end the paper by giving some approximation results and indicating some open problems related to the paper