英文标题：
《Fast, Accurate, Straightforward Extreme Quantiles of Compound Loss
Distributions》
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作者：
J.D. Opdyke
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最新提交年份：
2017
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英文摘要：
We present an easily implemented, fast, and accurate method for approximating extreme quantiles of compound loss distributions (frequency+severity) as are commonly used in insurance and operational risk capital models. The Interpolated Single Loss Approximation (ISLA) of Opdyke (2014) is based on the widely used Single Loss Approximation (SLA) of Degen (2010) and maintains two important advantages over its competitors: first, ISLA correctly accounts for a discontinuity in SLA that otherwise can systematically and notably bias the quantile (capital) approximation under conditions of both finite and infinite mean. Secondly, because it is based on a closed-form approximation, ISLA maintains the notable speed advantages of SLA over other methods requiring algorithmic looping (e.g. fast Fourier transform or Panjer recursion). Speed is important when simulating many quantile (capital) estimates, as is so often required in practice, and essential when simulations of simulations are needed (e.g. some power studies). The modified ISLA (MISLA) presented herein increases the range of application across the severity distributions most commonly used in these settings, and it is tested against extensive Monte Carlo simulation (one billion years\' worth of losses) and the best competing method (the perturbative expansion (PE2) of Hernandez et al., 2014) using twelve heavy-tailed severity distributions, some of which are truncated. MISLA is shown to be comparable to PE2 in terms of both speed and accuracy, and it is arguably more straightforward to implement for the majority of Advanced Measurement Approaches (AMA) banks that are already using SLA (and failing to take into account its biasing discontinuity).
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中文摘要：
我们提出了一种易于实现、快速且准确的方法，用于近似复合损失分布（频率+严重程度）的极端分位数，这是保险和运营风险资本模型中常用的方法。Opdyke（2014）的插值单损近似（ISLA）基于Degen（2010）广泛使用的单损近似（SLA），与竞争对手相比有两个重要优势：第一，ISLA正确地解释了SLA中的不连续性，否则会在有限和无限平均的条件下系统地显著偏离分位数（大写）近似值。其次，由于ISLA基于封闭形式近似，与其他需要算法循环的方法（例如快速傅立叶变换或Panjer递归）相比，它保持了SLA的显著速度优势。在模拟许多分位数（资本）估计时，速度很重要，这在实践中经常需要，在需要模拟时，速度也很重要（例如一些功率研究）。本文提出的改进ISLA（MISLA）增加了这些环境中最常用的严重性分布的应用范围，并使用十二个重尾严重性分布对其进行了广泛的蒙特卡罗模拟（十亿年的损失）和最佳竞争方法（Hernandez et al.，2014）进行了测试，其中一些被截断。MISLA在速度和准确度方面与PE2相当，可以说，对于大多数已经使用SLA（且未考虑其偏差不连续性）的高级测量方法（AMA）银行来说，实施MISLA更为简单。
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分类信息：

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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