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Hu, Yaozhong; Øksendal, Bernt

Fractional white noise calculus and applications to finance. (English) Zbl 1045.60072

Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6, No. 1, 1-32 (2003).
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.
Reviewer: George Stoica (Saint John)

Cited in 6 Reviews
Cited in 158 Documents

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.)

Keywords:

fractional Brownian motion; fractal Black-Scholes market
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\textit{Y. Hu} and \textit{B. Øksendal}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6, No. 1, 1--32 (2003; Zbl 1045.60072)
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References:

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