高维凸体的实用体积近似,用于投资组合相关性和金融危机建模

IF 0.4 4区 计算机科学 Q4 MATHEMATICS
Ludovic Calès , Apostolos Chalkis , Ioannis Z. Emiris , Vissarion Fisikopoulos
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引用次数: 0

摘要

我们研究了一般维多面体和更一般的凸体的体积计算,这些凸体是由一类平行超平面和另一类平行超平面或同心椭球体的单形相交所定义的。这种凸体出现在金融危机的建模和预测中。危机对经济(劳动力、收入等)的影响使其能够发现公众的主要利益,特别是决策者的主要利益。市场依赖的某些特征清楚地表明动荡时期。我们用联结关系来描述资产特征之间的关系;每个特征都是组合分量的线性或二次形式,因此可以通过计算凸体的体积来估计联结。我们设计并实现了精确和近似设置下的实用算法,并将它们实验并置,以研究精确和精度对速度的权衡。我们还通过实验找到了一种有效的参数调整方法,以获得对每个联结的概率密度的足够好的估计。我们的c++软件基于Eigen并可在github上获得,它在多达100个维度上被证明非常有效。我们的研究结果提供了新颖、有效的计算投资组合依赖关系的方法和金融危机的指标,这被证明可以正确识别过去的危机。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Practical volume approximation of high-dimensional convex bodies, applied to modeling portfolio dependencies and financial crises

We examine volume computation of general-dimensional polytopes and more general convex bodies, defined by the intersection of a simplex by a family of parallel hyperplanes, and another family of parallel hyperplanes or a family of concentric ellipsoids. Such convex bodies appear in modeling and predicting financial crises. The impact of crises on the economy (labor, income, etc.) makes its detection of prime interest for the public in general and for policy makers in particular. Certain features of dependencies in the markets clearly identify times of turmoil. We describe the relationship between asset characteristics by means of a copula; each characteristic is either a linear or quadratic form of the portfolio components, hence the copula can be estimated by computing volumes of convex bodies.

We design and implement practical algorithms in the exact and approximate setting, and experimentally juxtapose them in order to study the trade-off of exactness and accuracy for speed. We also experimentally find an efficient parameter-tuning to achieve a sufficiently good estimation of the probability density of each copula. Our C++ software, based on Eigen and available on github, is shown to be very effective in up to 100 dimensions. Our results offer novel, effective means of computing portfolio dependencies and an indicator of financial crises, which is shown to correctly identify past crises.

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来源期刊
CiteScore
1.60
自引率
16.70%
发文量
43
审稿时长
>12 weeks
期刊介绍: Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems. Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.
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