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).

翻译：损失准备金评估通常侧重于确定一个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，即通常会考虑不同模型的结果，有时还会将其合并。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取加权平均值。本文提出一个系统化的框架，用于客观地合并（即集成）多个随机损失准备金模型，从而有效利用不同模型的优势。与现有文献和实践相比，本框架包含两项主要创新。首先，我们的合并标准考虑了集成的完整分布特征，而不仅仅是中心估计——这在准备金评估背景下尤为重要。其次，我们的框架针对准备金数据的固有特征进行了定制。这些特征包括：事故期、发展期、日历期以及索赔成熟效应。关键的是，各事故期之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。我们通过一个复杂合成数据集对本框架进行了演示。结果显示，优化后的集成模型不仅优于（i）传统模型选择策略，也优于（ii）等权重集成模型。特别地，改进不仅体现在中心估计上，还体现在相关分位数上，例如准备金的第75百分位数——这通常是保险公司和监管机构共同关注的指标。