Stochastic calculus with respect to the fractional Brownian motion and applications

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Subfields: Finance

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Fractional Lévy processes with an application to long memory moving average processes (2006, methodology): “Recently, integration with respect to FBMs has been studied extensively and various approaches have been used to define a stochastic integral with respect to FBM (for a survey, see Nualart 2003).”
Arbitrage with fractional Brownian motion (2007, methodology): “Different approaches to the fractional Wick-Itô integral can be found in [18] via Malliavin calculus, [12] and [15] via white noise analysis, and [2] via a more elementary Stransform approach.”
Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case H=1/4 (2008, result): “Diﬀerentiating G n we obtain and, as a consequence, and, as a consequence, where r k,n is given by Remark that the ﬁrst sum in the right hand side of (3.12) is very similar to C n presented in Step 1.”
Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion (2008, background): “2 Preliminaries The reader is referred to [12] or [13] for any unexplained notion discussed in this section.”