多累积量张量分析在算法中的应用

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英文标题：
《The use of the multi-cumulant tensor analysis for the algorithmic
  optimisation of investment portfolios》
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作者：
Krzysztof Domino
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最新提交年份：
2016
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英文摘要：
  The cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares\' prices returns are good example of such data. The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability. Such algorithm is based on the Alternating Least Square method and involves the simultaneous minimisation 2\'nd -- 6\'th cumulants of the multidimensional random variable (percentage shares\' returns of many companies). Then the algorithm was tested during the recent crash on the Warsaw Stock Exchange. To determine incoming crash and provide enter and exit signal for the investment strategy the Hurst exponent was calculated using the local DFA. It was shown that introduced algorithm is on average better that benchmark and other portfolio determination methods, but only within examination window determined by low values of the Hurst exponent. Remark that the algorithm of is based on cumulant tensors up to the 6\'th order calculated for a multidimensional random variable, what is the novel idea. It can be expected that the algorithm would be useful in the financial data analysis on the world wide scale as well as in the analysis of other types of non Gaussian distributed data.
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中文摘要：
累积量分析在非高斯分布数据分析中起着重要作用。股票的价格回报率就是此类数据的一个很好的例子。本研究的目的是开发基于累积量的算法，并使用它来确定代表低可变性投资组合的特征向量。该算法基于交替最小二乘法，同时最小化多维随机变量（许多公司的股份收益率百分比）的第2~6个累积量。然后，该算法在最近华沙证券交易所的崩盘中进行了测试。为了确定即将到来的崩溃并为投资策略提供进入和退出信号，使用本地DFA计算赫斯特指数。结果表明，引入的算法平均优于基准和其他投资组合确定方法，但仅在由赫斯特指数低值确定的检查窗口内。请注意，的算法基于为多维随机变量计算的高达6阶的累积量张量，这是一个什么样的新想法。可以预期，该算法将在全球范围内的金融数据分析以及其他类型的非高斯分布数据分析中有用。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Computer Science        计算机科学
二级分类：Computational Engineering, Finance, and Science        计算工程、金融和科学
分类描述：Covers applications of computer science to the mathematical modeling of complex systems in the fields of science, engineering, and finance. Papers here are interdisciplinary and applications-oriented, focusing on techniques and tools that enable challenging computational simulations to be performed, for which the use of supercomputers or distributed computing platforms is often required. Includes material in ACM Subject Classes J.2, J.3, and J.4 (economics).
涵盖了计算机科学在科学、工程和金融领域复杂系统的数学建模中的应用。这里的论文是跨学科和面向应用的，集中在技术和工具，使挑战性的计算模拟能够执行，其中往往需要使用超级计算机或分布式计算平台。包括ACM学科课程J.2、J.3和J.4（经济学）中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Numerical Analysis        数值分析
分类描述：cs.NA is an alias for math.NA. Roughly includes material in ACM Subject Class G.1.
cs.na是Math.na的别名。大致包括ACM学科类G.1的材料。
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关键词：Applications SIMULTANEOUS Optimization Eigenvectors Mathematical