论文标题

保留保险损失的合奏分配预测

Ensemble distributional forecasting for insurance loss reserving

论文作者

Avanzi, Benjamin, Li, Yanfeng, Wong, Bernard, Xian, Alan

论文摘要

保留损失通常集中于确定可以产生卓越预测性能的单个模型。但是,不同的保留模型专门捕获损失数据的不同方面。实际上,这是从不同模型产生的,有时甚至组合的。例如,精算师通常会根据主观评估来获得各种保留模型的预测结果的加权平均值。 在本文中,我们提出了一个系统的框架,以客观地组合(即集合)多个_Stochastic_损失保留模型,以便可以有效利用不同模型提供的优势。与现有文献和实践相比,我们的框架包含了两项主要创新。首先,我们的标准模型组合考虑了集合的完整分布属性,而不仅仅是中心估计,这在保留环境中尤其重要。其次,我们的框架是针对保留数据固有的功能量身定制。这些包括事故,发展,日历和要求成熟效应。至关重要的是,事故期间数据的相对重要性和稀缺性使问题与统计学习中传统的结合技术不同。 使用复杂的合成数据集说明了我们的框架。在结果中,优化的合奏表现优于(i)传统的模型选择策略,以及(ii)同样加权的合奏。特别是,改进不仅发生了中央估计值,还可以进行相关的分位数,例如第75个储备金(通常是保险公司和监管机构的感兴趣)。本文开发的框架可以通过RCRAN可用的R软件包“ ADLP”来实现。

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.

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