Regularizing fractional Brownian motion with a view towards stock price modelling

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Dynamical pricing of weather derivatives (2002, background): “…in particular, trading, will result in price processes that can be modelled realistically by means of semimartingales is an issue that we cannot address here—this is a point that has been debated in the literature in the context of equity markets (Rogers 1997, Hu and Øksendal 1999, Cheridito 2001).”
Fractional Brownian motion (2006, background): “Let us mention the following surprising result proved by Cheridito in [8].”
Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4 (2003, background): “Interesting remarks have been recently done by [7] and [40].”
Arbitrage in fractional Brownian motion models (2003, background): “3) when H ∈ (12 , 1)), then for a real function f on R that is locally Lipschitz, the path-wise Riemann-Stieltjes integral ∫ t 0 f(Yu)dYu exists for all t ≥ 0 and equals F (Yt) − F (Y0), where F ′ = f .”