With insurers benefiting from ever-larger amounts of data of increasing complexity, we explore a data-driven method to model dependence within multilevel claims in this paper. More specifically, we start from a non-parametric estimator for Archimedean copula generators introduced by Genest and Rivest (1993), and we extend it to diverse flexible censoring scenarios using techniques derived from survival analysis. We implement a graphical selection procedure for copulas that we validate using goodness-of-fit methods applied to complete, single-censored, and double-censored bivariate data. We illustrate the performance of our model with multiple simulation studies. We then apply our methodology to a recent Canadian automobile insurance dataset where we seek to model the dependence between the activation delays of correlated coverages. We show that our model performs quite well in selecting the best-fitted copula for the data at hand, especially when the dataset is large, and that the results can then be used as part of a larger claims reserving methodology.

翻译：随着保险公司受益于日益庞大且复杂的海量数据，本文探索了一种基于数据驱动的方法来建模多层次索赔中的相依性。具体而言，我们从Genest和Rivest（1993）提出的阿基米德连接函数生成元的非参数估计量出发，利用生存分析中的技术将其扩展到多种灵活删失情形。我们实现了一种连接函数的图形选择程序，并通过应用于完全删失、单删失和双删失二元数据的拟合优度方法对其进行验证。通过多个仿真研究展示了模型性能。随后将所提方法应用于近期加拿大汽车保险数据集，旨在对相关险种激活延迟之间的相依性建模。结果表明，该方法在数据规模较大时能有效选择最佳拟合连接函数，且其结果可作为更广泛的索赔准备金评估方法的重要组成部分。