基于数值反演的总损失分布计算

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英文标题：
《Computing the aggregate loss distribution based on numerical inversion
  of the compound empirical characteristic function of frequency and severity》
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作者：
Viktor Witkovsky, Gejza Wimmer, Tomas Duby
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最新提交年份：
2017
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英文摘要：
  A non-parametric method for evaluation of the aggregate loss distribution (ALD) by combining and numerically inverting the empirical characteristic functions (CFs) is presented and illustrated. This approach to evaluate ALD is based on purely non-parametric considerations, i.e., based on the empirical CFs of frequency and severity of the claims in the actuarial risk applications. This approach can be, however, naturally generalized to a more complex semi-parametric modeling approach, e.g., by incorporating the generalized Pareto distribution fit of the severity distribution heavy tails, and/or by considering the weighted mixture of the parametric CFs (used to model the expert knowledge) and the empirical CFs (used to incorporate the knowledge based on the historical data - internal and/or external). Here we present a simple and yet efficient method and algorithms for numerical inversion of the CF, suitable for evaluation of the ALDs and the associated measures of interest important for applications, as, e.g., the value at risk (VaR). The presented approach is based on combination of the Gil-Pelaez inversion formulae for deriving the probability distribution (PDF and CDF) from the compound (empirical) CF and the trapezoidal rule used for numerical integration. The applicability of the suggested approach is illustrated by analysis of a well know insurance dataset, the Danish fire loss data.
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中文摘要：
提出并说明了一种通过组合和数值反演经验特征函数（CFs）来评估总损失分布（ALD）的非参数方法。这种评估ALD的方法基于纯粹的非参数考虑，即基于精算风险应用中索赔频率和严重程度的经验CFs。然而，这种方法可以自然地推广到更复杂的半参数建模方法，例如，通过合并严重度分布重尾的广义帕累托分布拟合，和/或通过考虑参数CFs（用于建模专家知识）和经验CFs（用于结合基于历史数据的知识-内部和/或外部）的加权混合。在此，我们提出了一种简单而有效的CF数值反演方法和算法，适用于评估ALD和对应用非常重要的相关利益度量，例如风险价值（VaR）。该方法基于Gil-Pelaez反演公式（用于从复合（经验）CF推导概率分布（PDF和CDF）和用于数值积分的梯形规则）的组合。通过对众所周知的保险数据集丹麦火灾损失数据的分析，说明了所建议方法的适用性。
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分类信息：

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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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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关键词：distribution Applications epidemiology Quantitative Application