Fractional stochastic differential equations with applications to finance

Abstract

In this paper we use a definition of the fractional stochastic integral given by Carmona et al.(2003) in [19] and develop a simple approximation method to study quasi-linear stochastic differential equations by fractional Brownian motion. We also propose a stochastic process, namely fractional semimartingale, to model for the noise driving in some financial models.