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：损失准备金通常侧重于识别一个能够产生优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。这一现实在实践中得到认可，即不同模型的结果常被考虑，有时甚至会进行组合。例如，精算师可能会根据主观判断，对不同损失准备金模型的预测结果进行加权平均。本文提出一个系统性框架，以客观的方式对多个_随机_损失准备金模型进行集成，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。首先，我们的标准不仅考虑集成的中心估计值，还考虑其完整的分布特性——这在准备金估计背景下尤为重要。其次，我们的框架针对准备金数据固有的特征进行了定制，例如事故期、发展期、日历期以及理赔成熟度效应。关键在于，不同事故期之间的数据相对重要性与稀疏性，使得此问题不同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该框架进行了验证。结果表明，优化后的集成模型优于（i）传统模型选择策略以及（ii）等权重集成模型。具体而言，改进不仅体现在中心估计值上，还体现在相关分位数上，例如准备金第75百分位数（通常对保险公司和监管机构均具有重要意义）。