英文标题：
《Practical volume computation of structured convex bodies, and an
  application to modeling portfolio dependencies and financial crises》
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作者：
Ludovic Cales, Apostolos Chalkis, Ioannis Z.Emiris, Vissarion
  Fisikopoulos
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最新提交年份：
2018
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英文摘要：
  We examine volume computation of general-dimensional polytopes and more general convex bodies, defined as 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. 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 constructed by computing volumes of convex bodies. We design and implement practical algorithms in the exact and approximate setting, we experimentally juxtapose them and study the tradeoff of exactness and accuracy for speed. We analyze the following methods in order of increasing generality: rejection sampling relying on uniformly sampling the simplex, which is the fastest approach, but inaccurate for small volumes; exact formulae based on the computation of integrals of probability distribution functions; an optimized Lawrence sign decomposition method, since the polytopes at hand are shown to be simple; Markov chain Monte Carlo algorithms using random walks based on the hit-and-run paradigm generalized to nonlinear convex bodies and relying on new methods for computing a ball enclosed; the latter is experimentally extended to non-convex bodies with very encouraging results. Our C++ software, based on CGAL and 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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中文摘要：
我们研究了一般维多面体和更一般的凸体的体积计算，定义为单纯形与一系列平行超平面和另一系列平行超平面或一系列同心椭球的相交。这种凸体出现在金融危机建模和预测中。危机对经济（劳动力、收入等）的影响使其能够检测出首要利益。市场依赖性的某些特征清楚地表明了动荡时期。我们通过copula描述资产特征之间的关系；每个特征要么是投资组合组件的线性形式，要么是二次形式，因此copula可以通过计算凸体的体积来构造。我们在精确和近似设置下设计并实现了实用的算法，我们对它们进行了实验并列，并研究了精确性和准确性与速度之间的权衡。为了增加通用性，我们分析了以下方法：拒绝采样依赖于均匀采样单纯形，这是最快的方法，但对小体积不准确；基于概率分布函数积分计算的精确公式；一种优化的劳伦斯符号分解方法，因为手边的多面体很简单；马尔可夫链蒙特卡罗算法采用随机游动，基于打了就跑的范式，推广到非线性凸体，并依赖于计算封闭球的新方法；后者通过实验扩展到非凸体，得到了非常令人鼓舞的结果。我们的C++软件基于CGAL和Eigen，在github上可用，在多达100个维度上都非常有效。我们的结果提供了计算投资组合相关性的新的、有效的方法，并提供了金融危机的指标，该指标被证明能够正确识别过去的危机。
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Computational Geometry        计算几何
分类描述：Roughly includes material in ACM Subject Classes I.3.5 and F.2.2.
大致包括ACM课程I.3.5和F.2.2中的材料。
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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