(资料分享)分数布朗运动(FBM)及其在金融中的应用文献

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分数布朗运动(FBM)及其在金融中的应用文献12篇

本帖隐藏的内容

汇总 Fractional Brownian Motion Modelling in Finance(12papers).zip (2.01 MB) 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

2014-8-31 15:54:48 上传

1 Fractional Brownian Motion and applications to fnancial Modelling.pdf (782.07 KB)

2014-8-31 15:51:50 上传

2 Parameter estimation of geometrically sampled fractionalBrownian traffic.pdf (154.22 KB)

2014-8-31 15:51:53 上传

3 Arbitrage in fractional Brownian motion.pdf (229.35 KB)

2014-8-31 15:51:54 上传

4 Inherent_Exclusion_of_Arbitrage FBM.pdf (207.83 KB)

2014-8-31 15:51:56 上传

7 A_random_walk_approximation_to_fractional_Brownian_motion.pdf (137.36 KB)

2014-8-31 15:51:59 上传

8 FRACTIONAL BROWNIAN MOTION theory and application.pdf (277.11 KB)

2014-8-31 15:52:03 上传

9 FBM in Finance.pdf (282 KB)

2014-8-31 15:52:09 上传

10 Stochastic Differential Equations Driven by FBM and SBM.pdf (241.49 KB)

2014-8-31 15:52:10 上传

11 Fractional Brownian motion Simulation Code and Method.pdf (23.72 KB)

2014-8-31 15:52:11 上传

12 fractional_Brownian_motion based on Wavelets.pdf (208.19 KB)

2014-8-31 15:52:12 上传

            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

            The main difference between fractional Brownian motion and regular Brownian motion is that while the increments in Brownian Motion are independent.

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关键词：分数布朗运动 资料分享 布朗运动 FBM 应用文 FBM 分数布朗运动

最近刚看过篇FBM的参考文献，但是文献里面读到错误。。。 所以看看其他的相关文档哈

及其在金融中的应用文献12篇

hyu9910 发表于 2014-8-31 16:18
最近刚看过篇FBM的参考文献，但是文献里面读到错误。。。 所以看看其他的相关文档哈

是的FBM也是最近二三十年兴起来的，FBM的发展还是很缓慢的啊，关于FBM连个First passage time理论都没有。。。。。。多多指教啊！！！

fantuanxiaot 发表于 2014-8-31 16:22
是的FBM也是最近二三十年兴起来的，FBM的发展还是很缓慢的啊，关于FBM连个First passage time理论都没有。 ...

指教做不到哈。 那也是我看过的第1篇FBM；尽管看到错误，但是不知道其影响程度。

hyu9910 发表于 2014-8-31 16:24
指教做不到哈。 那也是我看过的第1篇FBM；尽管看到错误，但是不知道其影响程度。

哎，我就是瞎子摸大象。。

3ks 4 sharing！

3ks 4 sharing！

感谢分享