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:损失保留一般侧重于确定单一模型,这种模型能够产生高超的预测性能。然而,不同的损失保留模型在捕捉损失数据的不同方面具有专长。在实践中,这得到确认,因为不同模型的结果往往被考虑,有时是合并的。例如,精算师可能从各种损失保留模型的预测结果中取一个加权平均数,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,客观地结合(例如,合用)多重_随机_损失保留模型,以便有效地利用不同模型所提供的优势。我们的框架与现有的文献和做法相比,包含两大主要创新。首先,我们的标准模型组合考虑的是各种模型的全面分布特性,而不仅仅是中央估计——这在保留背景下特别重要。第二,我们的框架是针对保留数据所固有的特征而设计的。例如,事故、发展、日历和成熟效应等。 关键是,不同事故时期的数据的相对重要性和稀缺性,使得问题与传统的堆积的文献和做法不同。首先,我们的标准模型的组合考虑的是,而不是核心估计的完全的完全的分布性特性。我们的数据选择框架以复杂的模型和精细的精细的精度为基础(我们的数据选择框架中,其精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细的精细。