The sensitivity of loss reserving techniques to outliers in the data or deviations from model assumptions is a well known challenge. It has been shown that the popular chain-ladder reserving approach is at significant risk to such aberrant observations in that reserve estimates can be significantly shifted in the presence of even one outlier. As a consequence the chain-ladder reserving technique is non-robust. In this paper we investigate the sensitivity of reserves and mean squared errors of prediction under Mack's Model (Mack, 1993). This is done through the derivation of impact functions which are calculated by taking the first derivative of the relevant statistic of interest with respect to an observation. We also provide and discuss the impact functions for quantiles when total reserves are assumed to be lognormally distributed. Additionally, comparisons are made between the impact functions for individual accident year reserves under Mack's Model and the Bornhuetter-Ferguson methodology. It is shown that the impact of incremental claims on these statistics of interest varies widely throughout a loss triangle and is heavily dependent on other cells in the triangle. Results are illustrated using data from a Belgian non-life insurer.

翻译：损失准备金技术对数据中的异常值或模型假设偏离的敏感性是众所周知的挑战。研究表明，流行的链梯法准备金方法在面对此类异常观测值时存在显著风险，即使仅有一个异常值，准备金估计也可能发生显著偏移。因此，链梯法准备金技术不具备稳健性。本文研究了Mack模型（Mack，1993）下准备金和预测均方误差的敏感性。通过推导影响函数实现，该函数通过计算相关统计量对观测值的一阶偏导数得到。当总准备金假设服从对数正态分布时，我们还提供并讨论了分位数的影响函数。此外，比较了Mack模型与Bornhuetter-Ferguson方法下单个事故年准备金的影响函数。结果表明，增量索赔对这些统计量的影响在整个损失三角中差异显著，且高度依赖于三角中的其他单元格。结果通过一家比利时非寿险保险公司的数据进行了说明。