共查询到20条相似文献,搜索用时 62 毫秒
1.
马芙玲 《数学的实践与认识》2017,(3):241-250
动量和反转效应普遍存在于证券市场,且会相互转换,但两者间相互转换的特征却鲜有人知.在多数派和少数派博弈的基础上,首次引入分形市场理论对投资者决策特征进行描述,据此建立了分形博弈过程,以分析动量和反转效应转换的统计特征.研究结果表明:在三种博弈机制下,分形博弈机制下的仿真收益率序列的统计分形特征更为接近实际序列的对数收益率序列,且动量和反转效应的相互转换与真实情况也异常相似,这体现了采用分形博弈分析动量和反转效应转换的有效性,为投资者构建有效的动量或反转投资策略提供了决策参考. 相似文献
2.
3.
4.
介绍了一种新的MFDFA(mu ltifractal detrended fluctuation analysis)方法,利用基于滑动窗技术的此MFDFA方法研究了上证综指日收益率序列的波动特征。结果表明:上证综指收益率序列具有多重分形特征,小幅波动具有持续性,大幅波动可能具有反持续性。 相似文献
5.
准确测量证券的风险和收益无论是对投资管理,还是对金融理论研究,甚至对理论成果向实践应用转化都至关重要。本文在证券价格具有分形特征的现实背景下,基于分形理论构建了分形期望和分形方差两个分形统计测度,以克服非分形统计测度在风险收益方面测不准或不可测的缺陷。在此基础上,应用分形统计测度构建了投资组合模型,给出了分形组合模型的解析解;随后,利用实证分析验证了分形统计测度在投资组合应用中的有效性。本文创新之处在于针对证券价格具有分形特征的现实背景构建了分形期望和分形方差两个分形统计测度;并基于分形统计测度构建了投资组合模型,将证券价格普遍存在的分形特征纳入投资组合的研究框架。 相似文献
6.
基于分形B-S定价模型的认购权证价格行为实证分析 总被引:1,自引:0,他引:1
针对证券收益率呈现"尖峰厚尾"的分布特征,在分析传统B-S权证定价模型的不足基础上,本文提出了基于分形理论的B-S权证定价模型,并利用分形B-S权证定价模型和传统B-S模型分析认购权证价格变化的行为。实证结果发现,两种模型的理论价格均低估了市场价格,且低估的程度具有显著统计性,其中以分形B-S模型评价结果最接近市场价格,评价绩效好。探讨影响分形B-S权证模型理论价格与市场价格差异的主要因素,结果发现距到期日时间的长短、价内外程度以及流动性在解释价差程度上具有统计的显著性。 相似文献
7.
黄静静 《数学的实践与认识》2014,(13)
运用重分形扩散熵分析方法来分析北京交通拥堵指数的长程相关性和重分形特征.方法综合使用了扩散技术和Renyi熵来研究北京交通拥堵指数的标度行为.由于交通拥堵指数序列具有明显的周期性,故先选用傅里叶滤波去除序列的周期性,再进行重分形扩散熵分析.实验结果表明北京交通拥堵指数序列的极端波动显示出反相关性,同时拥堵指数序列具有较弱的重分形特征. 相似文献
8.
准确地测量资产之间的相关性,是构建有效投资组合模型的前提.文章针对资产收益率存在分形相关性的现实情况,首先通过消除趋势交叉相关分析(DCCA)等方法,构建了分形相关性统计测度,用于测量资产之间的相关性;随后,通过将分形相关性统计测度纳入到收益-风险准则之中,构建了多时间标度前置下的投资组合模型Mean-PDCCA,即分形投资组合模型,并给出了模型的解析解;最后,实证分析发现,在资产收益率存在分形相关性的典型事实约束下,分形投资组合整体上优于经典投资组合,不仅能够提升投资业绩,还具有更好的稳健性,为投资者提供了有效的决策参考. 相似文献
9.
10.
上证综指分形特征研究 总被引:1,自引:0,他引:1
本文阐述了分形市场理论的基本思想和主要特征,运用重标极差(R/S)方法论对上证综指时间序列进行分形诊断,得出如下结论:①我国证券市场存在非周期循环,上证综指四种非周期循环的平均长度分别为858天、353天、246天和65天。②上证综指长周期Hurst指数值为0.561,市场具有“记忆”功能,信息对市场的影响具有持续性。③和西方市场相比,上证综指Hurst指数值较低,从而说明我国证券市场效率相对较低。 相似文献
11.
分形的广泛存在性已被普遍接受,然而分形维数的现有定义计算得到的结果是:不同的分形维数定义得到不同的分形维数值,甚至会出现不同的变化趋势,且在应用时使用的最小二乘回归结果不稳定,导致数值应用也会受影响,出现这些现象主要归咎于现有分形维数定义的严格性、抽象性以及分形图形的码尺效应.为避免这些问题,本文结合分形图形的长尾分布特征及自相似性提出一个新的分形量化形式——简便分形指数,并阐述了该定义背后的分形原理及计算方法,简便分形指数越大,形状复杂程度越高.最后本文利用岩石裂隙图像说明简便分形指数对不同裂隙网络复杂性描述的准确性,验证其作为分形图形量化方法的合理性及便利性. 相似文献
12.
Based on the construction of Fractal Interpolation Functions, a new construction of Fractal Interpolation Surfaces on arbitrary data is presented and some interesting properties of them are proved. Finally, a lower bound of their box counting dimension is provided. 相似文献
13.
The lexicographic sum of graphs is defined as follows. Let be a graph. With each associate a graph . The lexicographic sum of the graphs over is obtained from by substituting each by . Given distinct , we have all the possible edges in the lexicographic sum between and if , and none otherwise. When all the graphs are isomorphic to some graph , the lexicographic sum of the graphs over is called the lexicographic product of by and is denoted by . We say that a graph is fractal if there exists a graph , with at least two vertices, such that . There is a simple way to construct fractal graphs. Let be a graph with at least two vertices. The graph is defined on the set of functions from to as follows. Given distinct is an edge of if is an edge of , where is the smallest integer such that . The graph is fractal because . We prove that a fractal graph is isomorphic to a lexicographic sum over an induced subgraph of , which is itself fractal. 相似文献
14.
15.
《Applied Mathematical Modelling》2004,28(6):547-558
To the best of our knowledge, the analysis of densely folded media has not deserved special attention. The stress and strain analysis of this type of structures involves considerable difficulties concerning very strong non-linear effects. This paper presents a theory that could be classified as a geometric theory of folded media, in the sense that it ultimately leads to a kind of geometric constitutive law, or, in other words, a law that establishes the relationship between the geometry of the folded media and other variables such as the confinement capacity and the plastic strain energy. The discussion presented here is restricted to the particular case of compact balls produced by crushing together very thin plates or sheets. It is shown that both the geometry of the folded sheet and the plastic work density can be used as self-similarity tests. These criteria are equivalent for the case of thin plates or sheets made of the same material and with the same thickness. For the general case, the geometry of the folded sheet is not valid anymore as similarity criterion but there are strong arguments in favor of the plastic work density as a general criterion. If self-similarity is obtained for a ball set resulting from crumpling thin plates or sheets, it is possible to define two variables, the packing capacity and the slenderness ratio, that are related according to a power law. That is, the balls have a fractal representation. The power law scaling is derived from the mass conservation principle. The theory is claimed to be valid provided that certain assumptions referring to the geometry and material properties are satisfied. The results have shown that the theory is coherent and worthwhile of experimental validation. Some applications are suggested. A possible challenging investigation is related to the optimal geometry of biological membranes. 相似文献
16.
17.
A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function. 相似文献
18.
M. A. Navascués 《Complex Analysis and Operator Theory》2010,4(4):953-974
In the present article every complex square integrable function defined in a real bounded interval is approached by means
of a complex fractal function. The approximation depends on a partition of the interval and a vectorial parameter of the iterated
function system providing the fractal attractor. The original may be discontinuous or undefined in a set of zero measure.
The fractal elements can modify the features of the originals, for instance their character of smooth or non-smooth. The properties
of the operator mapping every function into its fractal analogue are studied in the context of the uniform and least square
norms. In particular, the transformation provides a decomposition of the set of square integrable maps. An orthogonal system
of fractal functions is constructed explicitly for this space. Sufficient conditions for the uniform convergence of the fractal
series expansion corresponding to this basis are also deduced. The fractal approximation of real functions is obtained as
a particular case. 相似文献
19.
Peter R. Massopust 《Journal of Geometry》1989,34(1-2):127-138
We show that the theory of iterated function systems (i.f.s.s) can be used to construct and geometrically describe Peano curves. We present this point of view by exhibiting i.f.s.s whose attractors are the graphs of some well-known Peano curves. 相似文献
20.
Fractal Hamilton-Jacobi-KPZ equations 总被引:1,自引:0,他引:1
Grzegorz Karch Wojbor A. Woyczynski 《Transactions of the American Mathematical Society》2008,360(5):2423-2442
Nonlinear and nonlocal evolution equations of the form , where is a pseudodifferential operator representing the infinitesimal generator of a Lévy stochastic process, have been derived as models for growing interfaces in the case when the continuous Brownian diffusion surface transport is augmented by a random hopping mechanism. The goal of this paper is to study properties of solutions to this equation resulting from the interplay between the strengths of the ``diffusive' linear and ``hyperbolic' nonlinear terms, posed in the whole space , and supplemented with nonnegative, bounded, and sufficiently regular initial conditions.