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Modeling very large losses

机译：建模非常大的损失

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摘要

In this paper, we present a simple probabilistic model for aggregating very large losses into a loss collection. This supposes that "standard" losses come in various possible sizes - small, moderate and large - which, fortunately, seem to occur with decreasing frequency. Standard modeling allows us to infer a probability distribution describing their occurrence. From the historical record, we know that very large losses do occur, albeit very rarely, yet they are not usually included in the available data sets. Such losses should be made part of the distribution for computation purposes. For example, to a bank they may helpful in the computation of economic or regulatory capital, while to an insurance company they may be useful in the computation of premiums of losses due to catastrophic events. We develop a simple modeling procedure that allows us to include very large losses in a loss distribution obtained from moderately sized loss data. We say that a loss is large when it is larger than the value-at-risk (VaR) at a high confidence level. The original and extended distributions will have the same VaR but quite different values of tail VaR (TVaR).
机译：在本文中，我们提出了一个简单的概率模型，用于将非常大的损失汇总到损失集合中。假设“标准”损失有各种可能的大小-小，中和大-幸运的是，这些损失似乎随着频率的降低而发生。标准建模允许我们推断描述其发生的概率分布。从历史记录中，我们知道确实会发生非常大的损失，尽管很少，但通常不会将其包括在可用数据集中。出于计算目的，应将此类损失纳入分配的一部分。例如，对于银行而言，它们可能有助于计算经济或监管资本，而对于保险公司而言，它们对于计算由于灾难性事件而引起的损失保费可能会有用。我们开发了一种简单的建模过程，使我们可以在从中等大小的损失数据获得的损失分布中包含非常大的损失。我们说，当损失大于高置信度下的风险价值（VaR）时，损失就很大。原始分布和扩展分布将具有相同的VaR，但尾部VaR（TVaR）的值将完全不同。

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