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Fractional Brownian Motion and Rough Models

The fractional Brownian motion (fBm) is an extension of the classical Brownian motion that allows its disjoint increments to be correlated. Its earliest mention in literature was in 1940 (see Kolmogorov (1940)). It was given the name of "fractional Brownian motion" by Mandelbrot and van Ness (1968).

FBm has proved to be a powerful tool in modeling. In recent years, fBm has found applications in very different areas of sciences and engineering, as for example surface growth (see for example Barábasi (1995)) or finance (see for example Mandelbrot (2001)). In recent years, the number of researchers interested in fBm (both from the theoretical and the applied point of view) has increased (see for example Nualart (2006) and the references therein). In mathematical biology, we remark its contribution to the study of cancer growth (see for example Brú et al. (2003)). In finance, we recall the study of new models based on fBm (see for example Rogers (1997), Biagini et al. (2008), Guasoni (2006), Cheridito (2003), Czichowsky and Schachermayer (2015), Comte and Renault (1998) or Comte, Coutin and Renault (2003)), Alòs, León and Vives (2007), Gatheral, Jaisson and Rosenbaum (2014), Bayer, Gatheral and Friz (2016)). The models introduced in these papers which are driven by fBm are used to describe the changes in the stock prices and/or the implied volatility.

The aim of this workshop is to invite top international researchers whose work is related to these recent papers to discuss both theoretical and applied aspects of these models.