A hierarchical reserving model for reported non-life insurance claims


Traditional non-life reserving models largely neglect the vast amount of information collected over the lifetime of a claim. This information includes covariates describing the policy (e.g. the value of the insured risk), claim cause (e.g. hail) as well as the detailed claim’s history (e.g. settlement, payment, involvement lawyer). We present the hierarchical reserving model as a modular framework for integrating a claim’s history and claim-specific covariates into the development process. Hierarchical reserving models decompose the joint likelihood of the development process over time. Moreover, they are tailored to the portfolio at hand by adding a layer to the model for each of the registered events (e.g. settlement, payment). Layers are modelled with classical techniques (e.g. generalized linear models) or machine learning methods (e.g. gradient boosting machines) and using claim-specific covariates. As a result of its flexibility, this framework incorporates many existing reserving models, ranging from aggregate models designed for runoff triangles to individual models using claim-specific covariates. This connection allows us to develop a data-driven strategy for choosing between aggregate and individual reserving; an important decision for reserving practitioners that is largely left unexplored in scientific literature. We illustrate our method with a case study on a real life insurance data set. This case study provides new insights in the covariates driving the development of claims and demonstrates the flexibility and robustness of the hierarchical reserving model over time.

On arxiv