Loss reserving generally focuses on identifying a single model that can generate superior predictive performance. However, different loss reserving models specialise in capturing different aspects of loss data. This is recognised in practice in the sense that results from different models are often considered, and sometimes combined. For instance, actuaries may take a weighted average of the prediction outcomes from various loss reserving models, often based on subjective assessments. In this paper, we propose a systematic framework to objectively combine (i.e. ensemble) multiple stochastic loss reserving models such that the strengths offered by different models can be utilised effectively. Criteria of choice consider the full distributional properties of the ensemble. A notable innovation of our framework is that it is tailored for the features inherent to reserving data. These include, for instance, accident, development, calendar, and claim maturity effects. Crucially, the relative importance and scarcity of data across accident periods renders the problem distinct from the traditional ensembling techniques in statistical learning. Our ensemble reserving framework is illustrated with a complex synthetic dataset. In the results, the optimised ensemble outperforms both (i) traditional model selection strategies, and (ii) an equally weighted ensemble. In particular, the improvement occurs not only with central estimates but also relevant quantiles, such as the 75th percentile of reserves (typically of interest to both insurers and regulators).
翻译:保留损失通常侧重于确定单一模型,这种模型能够产生高超的预测性性能。然而,不同的保留损失模型在获取损失数据的不同方面具有专长。这在实践中得到承认,因为通常会考虑,有时会结合不同模型的结果。例如,精算师可能采用各种损失保留模型的预测结果加权平均数,通常以主观评估为基础。在本文件中,我们提出了一个系统框架,客观地将多种随机损失模型(即共通)结合起来,以便有效地利用不同模型提供的强项。选择标准考虑了共同值的全部分布特性。我们框架的一个显著创新是,它适合保留数据所固有的特征,例如,事故、开发、日历和索赔到期效应。关键的是,不同事故期间数据的相对重要性和稀缺性使问题有别于统计学习中传统的混合技术。我们的组合保留框架用复杂的合成数据来说明。在结果中,选择的组合值是组合值的完全分布性特性,我们框架的一个显著创新是,我们框架是针对保留数据所固有的特性的特征。例如,我们框架是针对保留数据所固有的特性,而选择的组合值是用于保留数据所固有的特性的特性,例如事故、发展、日历的精度的精度的精度的精度的精度的精度的精度的精度是核心的精度的精度的精度,这种精度的精度的精度的精度,以及精度的精度的精度的精度的精度的精度的精度的精度是,这种精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度和精度是精度是精度的精度的精度的精度的精度的精度的精度的精度的精度是的精度是的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度的精度是精度是精度的精度的精度的精度,是精度的精度的精度的精度的精