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. Our framework contains two main innovations compared to existing literature and practice. Firstly, our criteria model combination considers the full distributional properties of the ensemble and not just the central estimate - which is of particular importance in the reserving context. Secondly, 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 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). The framework developed in this paper can be implemented thanks to an R package, `ADLP`, which is available from CRAN.

翻译：损失准备金评估通常侧重于识别能够产生卓越预测性能的单一模型。然而，不同的损失准备金模型擅长捕捉损失数据的不同方面。实践中已认识到这一点，因此通常会考虑不同模型的结果，有时甚至进行组合。例如，精算师可能会基于主观判断对不同损失准备金模型的预测结果进行加权平均。本文提出一个系统框架，以客观方式组合（即集成）多个随机损失准备金模型，从而有效利用不同模型提供的优势。与现有文献和实践相比，我们的框架包含两大创新点。首先，我们的模型组合准则考虑了集成的完整分布特性，而不仅仅是中心估计值——这在准备金评估背景下尤为重要。其次，我们的框架专门针对准备金数据固有特征进行设计，包括事故期、进展期、日历期及索赔成熟度效应等。关键在于，不同事故期间数据的相对重要性和稀缺性使得该问题有别于统计学习中的传统集成技术。我们通过一个复杂的合成数据集展示了该框架的应用效果。结果显示，优化后的集成模型在以下两方面均表现更优：（1）传统模型选择策略；（2）等权重集成模型。特别值得注意的是，改进不仅体现在中心估计值上，还体现在相关分位数上，例如准备金分布的75%分位数（通常为保险公司和监管机构关注的重点）。本文开发的框架可通过R软件包`ADLP`实现，该包可从CRAN获取。