Functional Profile Techniques for Claims Reserving

Abstract

One of the most fundamental tasks in non-life insurance, done on regular basis, is risk reserving assessment analysis, which amounts to predict stochastically the overall loss reserves to cover possible claims. The most common reserving methods are based on different parametric approaches using aggregated data structured in the run-off triangles. In this paper, we propose a rather non-parametric approach, which handles the underlying loss development triangles as functional profiles and predicts the claim reserve distribution through permutation bootstrap. Three competitive functional-based reserving techniques, each with slightly different scope, are presented; their theoretical and practical advantages – in particular, effortless implementation, robustness against outliers, and wide-range applicability – are discussed. Theoretical justifications of the methods are derived as well. An evaluation of the empirical performance of the designed methods and a full-scale comparison with standard (parametric) reserving techniques are carried on several hundreds of real run-off triangles against the known real loss outcomes. An important objective of the paper is also to promote the idea of natural usefulness of the functional reserving methods among the reserving practitioners.

Heat Equation as a Tool for Outliers Mitigation in Run-Off Triangles for Valuing the Technical Provisions in Non-Life Insurance Business

“…A popular method that generates a simulated prediction distribution to obtain the standard errors of well-specified models is bootstrapping (Verdonck et al 2009). This method has already been considered in the area of claims reserving by (England and Verrall 1999;Lowe 1994;Maciak et al 2022;Zaçaj et al 2022). Several authors ( Peremans et al 2017;Verdonck et al 2009) applied robust bootstrap procedures for the chain-ladder method.…”