By: João Guerra
At: Instituto de Investigação Interdisciplinar, B3-01
The fractional Brownian motion (fBm) is a generalization of the standard Brownian motion in the sense that it is a Gaussian process with correlated increments. The fBm satisfies self-similarity and long-range dependence properties. These properties make fBm a suitable driving process in applications to finance and network traffic analysis. In order to develop these applications, one needs to construct a stochastic calculus with respect to fBm since it is not a semimartingale and we cannot use the classical ItÃ´ stochastic calculus. We will discuss a possible approach to the construction of a stochastic calculus for fBm and some applications to finance.