英文标题：
《Keep It Real: Tail Probabilities of Compound Heavy-Tailed Distributions》
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作者：
Igor Halperin
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最新提交年份：
2017
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英文摘要：
  We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation of the tail probability of a compound distribution in the form of a rapidly convergent one-dimensional integral involving a discontinuity of the imaginary part of its moment generating function across a branch cut. The latter integral can be evaluated in quadratures, or alternatively represented as an asymptotic expansion. Our approach thus offers a viable (especially at high percentile levels) alternative to more standard methods such as Monte Carlo or the Fast Fourier Transform, traditionally used for such problems. As a practical application, we use our method to compute the operational Value at Risk (VAR) of a financial institution, where individual losses are modeled as spliced distributions whose large loss components are given by power-law or lognormal distributions. Finally, we briefly discuss extensions of the present formalism for calculation of tail probabilities of compound distributions made of compound distributions with heavy tails.
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中文摘要：
我们提出了一种计算复合分布尾部概率的分析方法，其单个分量具有重尾。我们的方法基于轮廓积分法，并以快速收敛的一维积分形式表示复合分布的尾部概率，该一维积分涉及其矩母函数的虚部在分支切口上的不连续性。后一个积分可以求积，也可以表示为渐近展开。因此，我们的方法提供了一种可行的（尤其是在高百分位水平上）替代更标准的方法，如蒙特卡罗或快速傅立叶变换，传统上用于此类问题。作为一个实际应用，我们使用我们的方法计算金融机构的操作风险价值（VAR），其中个人损失被建模为拼接分布，其大损失分量由幂律分布或对数正态分布给出。最后，我们简要讨论了现有形式的扩展，用于计算由重尾复合分布构成的复合分布的尾部概率。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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一级分类：Statistics        统计学
二级分类：Computation        计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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