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Fractional white noise calculus and applications to finance. (English) Zbl 1045.60072
The authors develop a fractional white noise calculus and apply this to markets modelled by Wick-Itō type stochastic differential equations driven by fractional Brownian motion with Hurst parameter between \(1/2\) and \(1\). The market in this case is complete, and explicit formulae for the price and replicating portfolio of a European option are presented.

MSC:
60H40 White noise theory
60H05 Stochastic integrals
60G15 Gaussian processes
60G22 Fractional processes, including fractional Brownian motion
91G20 Derivative securities (option pricing, hedging, etc.)
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