Traditional techniques for calculating outstanding claim liabilities such as the chain ladder are notoriously at risk of being distorted by outliers in past claims data. Unfortunately, the literature in robust methods of reserving is scant, with notable exceptions such as Verdonck and Debruyne (2011) and Verdonck and Van Wouwe (2011). In this paper, we put forward two alternative robust bivariate chain-ladder techniques to extend the approach of Verdonck and Van Wouwe (2011). The first technique is based on Adjusted Outlyingness (Hubert and Van der Veeken, 2008) and explicitly incorporates skewness into the analysis whilst providing a unique measure of outlyingness for each observation. The second technique is based on bagdistance (Hubert et al., 2016) which is derived from the bagplot however is able to provide a unique measure of outlyingness and a means to adjust outlying observations based on this measure. Furthermore, we extend our robust bivariate chain-ladder approach to an N-dimensional framework. The implementation of the methods, especially beyond bivariate, is not trivial. This is illustrated on a trivariate data set from Australian general insurers, and results under the different outlier detection and treatment mechanisms are compared.

翻译：计算未决赔款准备金的传统技术（如链梯法）极易因历史赔款数据中的离群点而产生失真。遗憾的是，关于鲁棒准备金方法的文献甚少，仅有的例外包括Verdonck和Debruyne（2011）以及Verdonck和Van Wouwe（2011）的研究。本文提出两种替代性鲁棒双变量链梯技术，以扩展Verdonck和Van Wouwe（2011）的方法。第一种技术基于调整离群度（Hubert和Van der Veeken，2008），在分析中显式纳入偏度，同时为每个观测值提供唯一的离群度量。第二种技术基于袋距离（Hubert等，2016），该距离源于袋图，能够提供唯一的离群度量，并据此调整离群观测值。此外，我们将鲁棒双变量链梯方法扩展至N维框架。相关方法的实现（尤其在超越双变量情形时）并非易事。本文以澳大利亚普通保险公司的三变量数据集为例进行说明，并对不同离群点检测与处理机制下的结果进行比较。