Simulations of Bivariate Archimedean Copulas from Their Nonparametric Generators for Loss Reserving under Flexible Censoring

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 article. More specifically, we extend the nonparametric estimator for Archimedean copula generators and graphical copula selection procedure introduced by Genest and Rivest to flexible censoring scenarios, using techniques derived from survival analysis. We then propose an alternative method that forgoes any parametric assumption by directly simulating from the estimator of the generator function, using algorithms based on inverse Laplace-Stieltjes transforms. In this article, we focus on a bivariate application and illustrate the performance of our approach with an analysis of a recent Canadian automobile insurance dataset, in which we seek to incorporate the dependence between the activation delays of correlated coverages in a claims reserving framework. We explore the impact on the reserve estimates of performing simulations directly from our nonparametric estimator of the Archimedean copula generator function compared to simulations from a known parametric copula.