摘要翻译：
通常，操作风险损失报告高于某个阈值。本文研究了在较宽的分布参数和截断水平范围内，忽略数据截断对操作风险年损失分布的0.999分位点的影响。损失频率和严重程度分别用泊松分布和对数正态分布建模。研究了两种忽略数据截断的情况：“朴素模型”--在半无限正区间上拟合有支撑的对数正态分布；“移位模型”--拟合移位到截断水平的对数正态分布。对于所有实际情况，“朴素模型”都会导致对0.999分位数的低估（这可能是严重的）。“移位模型”高估了0.999分位数，除了一些对大截断水平的小低估情况。资本费用的保守估计通常是可以接受的，使用“转移模型”是合理的，而不应允许使用“朴素模型”。然而，如果考虑到参数不确定性（在实践中经常被忽略），“移位模型”可能导致资本费用的严重低估。并用一个实际例子对此进行了说明。
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英文标题：
《Addressing the Impact of Data Truncation and Parameter Uncertainty on
  Operational Risk Estimates》
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作者：
Xiaolin Luo, Pavel V. Shevchenko and John B. Donnelly
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最新提交年份：
2009
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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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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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英文摘要：
  Typically, operational risk losses are reported above some threshold. This paper studies the impact of ignoring data truncation on the 0.999 quantile of the annual loss distribution for operational risk for a broad range of distribution parameters and truncation levels. Loss frequency and severity are modelled by the Poisson and Lognormal distributions respectively. Two cases of ignoring data truncation are studied: the "naive model" - fitting a Lognormal distribution with support on a positive semi-infinite interval, and "shifted model" - fitting a Lognormal distribution shifted to the truncation level. For all practical cases, the "naive model" leads to underestimation (that can be severe) of the 0.999 quantile. The "shifted model" overestimates the 0.999 quantile except some cases of small underestimation for large truncation levels. Conservative estimation of capital charge is usually acceptable and the use of the "shifted model" can be justified while the "naive model" should not be allowed. However, if parameter uncertainty is taken into account (in practice it is often ignored), the "shifted model" can lead to considerable underestimation of capital charge. This is demonstrated with a practical example.
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PDF链接：
https://arxiv.org/pdf/0904.2910