分数布朗运动(FBM)及其在金融中的应用文献12篇

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Fractional Brownian Motion Modelling in Finance(12papers).zip
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本附件包括：

• 12 fractional_Brownian_motion based on Wavelets.pdf
• 1 Fractional Brownian Motion and applications to fnancial Modelling.pdf
• 2 Parameter estimation of geometrically sampled fractionalBrownian traffic.pdf
• 3 Arbitrage in fractional Brownian motion.pdf
• 4 Inherent_Exclusion_of_Arbitrage FBM.pdf
• 5 Fractional Brownian motion stochastic calculus.pdf
• 6 Option_Pricing_in_a_Fractional_Brownian_Motion.pdf
• 7 A_random_walk_approximation_to_fractional_Brownian_motion.pdf
• 8 FRACTIONAL BROWNIAN MOTION theory and application.pdf
• 9 FBM in Finance.pdf
• 10 Stochastic Differential Equations Driven by FBM and SBM.pdf
• 11 Fractional Brownian motion Simulation Code and Method.pdf

1 Fractional Brownian Motion and applications to fnancial Modelling.pdf
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2 Parameter estimation of geometrically sampled fractionalBrownian traffic.pdf
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3 Arbitrage in fractional Brownian motion.pdf
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4 Inherent_Exclusion_of_Arbitrage FBM.pdf
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7 A_random_walk_approximation_to_fractional_Brownian_motion.pdf
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8 FRACTIONAL BROWNIAN MOTION theory and application.pdf
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9 FBM in Finance.pdf
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10 Stochastic Differential Equations Driven by FBM and SBM.pdf
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11 Fractional Brownian motion Simulation Code and Method.pdf
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12 fractional_Brownian_motion based on Wavelets.pdf
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            A normalized fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of  Brownian motion without independent increments. It is a continuous-time Gaussian process BH(t) on [0, T], which starts at zero, has expectation zero for all t in [0, T], and has the following covariance function:

.

            where H is a real number in (0, 1), called the Hurst index or Hurst parameter associated with the fractional Brownian motion. The Hurst exponent describes the raggedness of the resultant motion, with a higher value leading to a smoother motion. It was introduced by Mandelbrot & van Ness (1968).

            The value of H determines what kind of process the fBm is:if H = 1/2 then the process is in fact a Brownian motion or Wiener process;if H > 1/2 then the increments of the process are positively correlated;if H < 1/2 then the increments of the process are negatively correlated.The increment process, X(t) = BH(t+1) − BH(t), is known as fractional Gaussian noise.

            Prior to the introduction of the fractional Brownian motion,Lévy (1953) used the Riemann–Liouville fractional integral to define the process:

            where integration is with respect to the white noise measure dB(s). This integral turns out to be ill-suited to applications of fractional Brownian motion.

             The idea instead is to use a different fractional integral of white noise to define the process: the Weyl integral