通过广义贝叶斯模型平均实现灵活的极端阈值
Flexible extreme thresholds through generalised Bayesian model averaging
AI总结：
本文提出一种误差集成贝叶斯模型平均算法，通过结合混合模型检测适应预测变量的异质最优阈值，以提高高严重性索赔损失建模的准确性并降低对阈值选择的敏感性。
摘要：
保险产品经常涵盖来自各种来源的重大索赔。为了准确模拟这些产品的损失，精算模型必须考虑高严重性索赔。一种广泛使用的策略是应用混合模型，将一种分布拟合到低于给定阈值的损失，并使用极值理论对超额损失进行建模。然而，选择适当的阈值仍然是一个悬而未决的问题，没有普遍认可的解决方案。贝叶斯模型平均（BMA）提供了一种有前途的替代方案，可以同时考虑多个阈值。在本文中，我们展示了误差集成BMA算法能够通过混合模型的组合，有效检测适应预测变量的异质最优阈值。该方法通过捕捉完整的损失分布并降低对阈值选择的敏感性来提高模型准确性。我们使用模拟研究和对一家加拿大保险公司汽车索赔数据集的应用来验证所提出的方法。作为特例，我们还研究了同质设置，其中选择单个最优阈值，并将其应用于精算数据集的基于拟合优度检验的自动选择算法进行比较。
英文摘要：
Insurance products frequently cover significant claims arising from a variety of sources. To model losses from these products accurately, actuarial models must account for high-severity claims. A widely used strategy is to apply a mixture model, fitting one distribution to losses below a given threshold and modeling excess losses using extreme value theory. However, selecting an appropriate threshold remains an open question with no universally agreed-upon solution. Bayesian Model Averaging (BMA) provides a promising alternative by enabling the simultaneous consideration of multiple thresholds. In this paper, we show that an error integration BMA algorithm can effectively detect heterogeneous optimal thresholds that adapt to predictive variables through the combination of mixture models. This method enhances model accuracy by capturing the full loss distribution and lessening sensitivity to threshold choice. We validate the proposed approach using simulation studies and an application to an automobile claims dataset from a Canadian insurer. As a special case, we also study the homogeneous setting, where a single optimal threshold is selected, and compare it to automatic selection algorithms based on goodness-of-fit tests applied to an actuarial dataset.
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