英文标题：
《Large deviations for risk measures in finite mixture models》
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作者：
Valeria Bignozzi, Claudio Macci, Lea Petrella
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最新提交年份：
2018
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英文摘要：
  Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is evaluated on the estimated mixture instead of the (unknown) true one, then it is important to investigate the committed error. In this paper we study the asymptotic behaviour of estimated risk measures, as the data sample size tends to infinity, in the fashion of large deviations. We obtain large deviation results by applying the contraction principle, and the rate functions are given by a suitable variational formula; explicit expressions are available for mixtures of two models. Finally, our results are applied to the most common risk measures, namely the quantiles, the Expected Shortfall and the shortfall risk measures.
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中文摘要：
由于其异质性，保险风险可以适当地描述为不同固定模型的混合，其中分配给每个模型的权重可以根据可用数据样本进行经验估计。如果风险度量是根据估计的混合而不是（未知的）真实混合来评估的，那么调查犯下的错误很重要。在本文中，我们研究了当数据样本量趋于无穷大时，以大偏差的方式估计的风险度量的渐近行为。应用收缩原理得到了大偏差结果，并通过适当的变分公式给出了速率函数；显式表达式可用于两个模型的混合。最后，我们的结果应用于最常见的风险度量，即分位数、预期短缺和短缺风险度量。
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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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