财产与意外伤害保险中损失发展模式的功能性分析 (Functional Analysis of Loss-development Patterns in P&C Insurance)

from arxiv, 34 pages. Keywords: loss development; loss reserving; incremental loss ratios; unsupervised learning; functional data; functional depth; outlier detection; IBNR

We analyze loss development in NAIC Schedule P loss triangles using functional data analysis methods. Adopting the functional viewpoint, our dataset comprises 3300+ curves of incremental loss ratios (ILR) of workers' compensation lines over 24 accident years. Relying on functional data depth, we first study similarities and differences in development patterns based on company-specific covariates, as well as identify anomalous ILR curves. The exploratory findings motivate the probabilistic forecasting framework developed in the second half of the paper. We propose a functional model to complete partially developed ILR curves based on partial least squares regression of PCA scores. Coupling the above with functional bootstrapping allows us to quantify future ILR uncertainty jointly across all future lags. We demonstrate that our method has much better probabilistic scores relative to Chain Ladder and in particular can provide accurate functional predictive intervals.

翻译：我们采用功能性数据分析方法，分析了NAIC附表P损失三角形中的损失发展情况。从功能性视角出发，我们的数据集包含超过3300条工人赔偿险种在24个事故年度内的增量损失率曲线。基于功能性数据深度，我们首先研究了基于公司特定协变量的发展模式之间的相似性与差异，并识别了异常的增量损失率曲线。这些探索性发现为本文后半部分开发的概率预测框架提供了动机。我们提出了一种功能性模型，用于基于主成分分析得分的偏最小二乘回归来完成部分已发展的增量损失率曲线。将上述方法与功能性自举法结合，使我们能够量化所有未来滞后期的增量损失率联合不确定性。我们证明，相对于链梯法，我们的方法在概率评分方面表现更优，尤其能够提供准确的功能性预测区间。