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A general fractional white noise theory and applications to finance. (English) Zbl 1069.91047

In this paper, the authors present a new framework for a fractional Browinian motion in which processes with all Hurst indices in \((0,1)\) can be considered on the space of tempered distributions under the same probability measure. A key result is the generalized Itô isometry for stochastic integrals with respect to the fractional Brownian motion. The paper extends the contribution by Hu and Øksendal (2000) with the Hurst index in \((1/2,1)\). Option pricing formulas in a multiple fractional Brownian Black-Scholes market are derived.

MSC:

91B28 Finance etc. (MSC2000)
91B70 Stochastic models in economics
60H40 White noise theory
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