(Geometric Brownian Motion)是一种连续时间随机过程,通常用来描述某些财务和经济学领域中的现象,比如股票价格的变化或汇率的波动等。它的特点是在每个时间段内的增长率与当前值成比例,而且这个比例服从正态分布。 几何布朗运动可以用如下的随机微分方程来表示: GBM 其中,St表示在时间 t 时刻的股票价格或其他随机变量...
Geometric Brownian Motion Model in Financial Market Zhijun Yang Faculty Adivisor: David Aldous In the modeling of financial market, especially stock market, Brownian Motion play a significant role in building a statisitcal model. In this section, I will explore some of the technique to buil...
ylabel('t');zlabel('PDF');title('Geometric Brownian Motion PDF');几何布朗运动在金融学中有广泛应用，用于描述股票价格、汇率等金融资产波动，以及期权定价等研究。
doi:10.1007/978-3-0348-8163-0_17Sigman, KarlKarl, Sigman. 2006. Geometric Brownian Motion.Columbia University, New York.Karl Sigman, Geometric Brownian motion.Geometric Brownian Motion[OL].http://www.math.duke.edu/education/ccp/materials/fin/gbm/ contents.html,2004....
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2024. Sub mixed fractional Brownian motion and its application to finance. Chaos, Solitons Fractals 184: 114968. DOI: 10.1016/j.chaos.2024.114968 (Open in a new window)Google Scholar Malkiel, B. G. 2003. The efficient market hypothesis and its critics. Journal Economics perspectives. 17(1)...
[ hal82 , nun15 ]. 1.2 fractional brownian motion. one notable feature of theorems 1 and 2 is that while the expected count of squarefrees in a short interval (or likewise arithmetic progression) is of order h , the variance of these counts is of order \(h^{1/2}\) . for many ...
Next PDF/EPUB Tools Share Cite Recommend Abstract Universal constructions of univariate and bivariate Gaussian distributions, as transformations of diffuse probability distributions via, respectively, plane- and space-filling fractal interpolating functions and the central limit theorems that they imply, are ...
Chernov, N., Dolgopyat, D.: Brownian Brownian Motion—I. Memoirs AMS 198(927), 193 pp (2009) Chernov, N., Eyink, G., Lebowitz, J., Sinai, Ya.: Steady-state electrical conduction in the periodic Lorentz gas. Commun. Math. Phys. 154(3), 569–601 (1993) Article ADS MathSciNet MA...
(15) The analogous result in the limit of continuous time rebalancing has been obtained previously by Fernholz and Shay (1982), who showed that it is exact when the prices follow geometric Brownian motion. A different form of the same result may be obtained by using i Xi = 1 in the ...