基于提升小波变换的布朗运动的生成算法
Generated Algorithm for Brown Motion Based on Lifting Wavelet Transform
DOI: 10.12677/pm.2024.143099, PDF,   
作者: 曹航宾：新疆师范大学数学科学学院，新疆 乌鲁木齐；周小辉：上海财经大学浙江学院，浙江 金华
关键词: 分形整合过程；提升小波变换；Brown运动；Fractal Integration Process； Improve Wavelet Transform； Brown Motion
摘要: 文中基于提升小波系数，首先提出了一种生成标准正态随机数的新方法与多维Brown运动生成算法，且给出了1维，2维与3维情形的模拟。然后将小波系数应用于金融模型中，利用小波系数讨论了典范双因子Vasicek模型。最后给出了显式表达式和数值模拟。
Abstract: Based on the wavelet coefficients, a new method for generating standard normal random numbers and a new generation algorithm for multi-dimensional Brown motion are proposed in this paper. And some numerical simulations are given in one-dimensional, two-dimensional and three-dimensional cases. Then the wavelet coefficients are applied in the financial model. The canonical two-factor Vasicek model is discussed by wavelet coefficients. The explicit expressions and numerical simulation are given finally.
文章引用：曹航宾, 周小辉. 基于提升小波变换的布朗运动的生成算法[J]. 理论数学, 2024, 14(3): 201-210. https://doi.org/10.12677/pm.2024.143099

参考文献

[1] Jensen, M.J. (1999) Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter. Journal of Forecasting, 18, 17-32. [Google Scholar] [CrossRef] 
[2] Masdemont, J.J. and Ortiz-Gracia, L. (2011) Haar Wavelets-Based Approach for Quantifying Credit Portfolio Losses. Quantitative Finance, 14, 1587-1595. [Google Scholar] [CrossRef] 
[3] Gallegati, M. (2014) Wavelet Applications in Economics and Finance. Springer, Berlin. [Google Scholar] [CrossRef] 
[4] 姜礼尚. 期权定价的数学模型和方法[M]. 北京: 高等教育出版社, 2008.
[5] 陈启宏, 陈迪华(译). 金融随机分析(第二卷) [M]. 上海: 上海财经大学出版社, 2015.
[6] 姜礼尚, 徐承龙, 任学敏, 李少华. 金融衍生品产品定价的数学模型与案例分析[M]. 第二版. 北京: 高等教育出版社, 2013.
[7] Zhou, X.H. and Gu, G.D. (2022) An Algorithm of Generating Random Number by Wavelet Denoising Method and Its Application. Computational Statistics, 37, 107-124. [Google Scholar] [CrossRef] 
[8] Daubechies, I. (1992) Ten Lectures on Wavelets. PA SIAM Press, Philadelphia. [Google Scholar] [CrossRef] 
[9] Zhou, X.H. and Wang, B.Q. (2018) Wavelet Analysis on Some Smooth Surface with Non-Zero Constant Gaussian Curvature. International Journal of Wavelets Multiresolution & Information Processing, 16, Article ID 185007. [Google Scholar] [CrossRef] 
[10] Sweldens, W. (1996) The Lifting Scheme: A Custom-Design Construction of Biorthogonal Wavelets. Applied and Computational Harmonic Analysis, 3, 186-200. [Google Scholar] [CrossRef] 
[11] Zhou, X. and Gu, G. (2020) The Construction of Multi-Wavelets with Matrix Dilation via the Lifting Scheme with Several Steps. Lecture Notes in Electrical Engineering, 592, 11-23. [Google Scholar] [CrossRef] 
[12] Fatichi, S. (2009) Matlab Routine for Time Series Simulation with ARFIMA Models.
https://ww2.mathworks.cn/matlabcentral/fileexchange/25611-arfima-simulations
[13] In, F. and Kim, S. (2012) An Instruction to Wavelet Theory in Finance: A Wavelet Multiscale Approach. World Scientific, Singapore, 212. [Google Scholar] [CrossRef] 
[14] Rometsch, R.M.X. (2011) A Wavelet Tour of Option Pricing. Dissertation, Universität Ulm Fakultät für Mathematik und Wirtschaftswissenschaften, Ulm.

为你推荐