Methods and Applications of Analysis

Volume 10 (2003)

Number 3

MINIMAL VARIANCE HEDGING FOR FRACTIONAL BROWNIAN MOTION

Pages: 347 – 362

DOI: http://dx.doi.org/10.4310/MAA.2003.v10.n3.a2

Authors

FRANCESCA BIAGINI

BERNT ØKSENDAL

Abstract

We discuss the extension to the multi-dimensional case of the Wick-Itô integral with respect to fractional Brownian motion, introduced by [6] in the 1-dimensional case. We prove a multidimensional Itô type isometry for such integrals, which is used in the proof of the multi-dimensional Itô formula. The results are applied to study the problem of minimal variance hedging in a market driven by fractional Brownian motions.

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