BFS 2002 

Poster Presentation 
Francesca Biagini, Bernt Øksendal
Because of its properties (persistence/antipersistence and selfsimilarity), the fractional Brownian motion (fBm) has been suggested as a useful mathematical tool in many applications, including finance.
In this paper, we discuss the extension to the multidimensional case of the WickIto integral with respect to fractional Brownian motion and apply this approach to study the problem of minimal variance hedging in a (possibly incomplete) market driven by mdimensional fBm. The meanvariance optimal strategy is obtained by projecting the option value on a suitable space of stochastic integrals with respect to the fBm, which represents the attainable claims.
Here we prove first a multidimensional Ito type isometry for such integrals, which is used in the proof of the multidimensional Ito formula. These results are then applied in order to provide a necessary and sufficient characterization of the optimal strategy as a solution of a differential equation involving Malliavin derivatives.