A generalized reserving model: bridging the gap between pricing and individual reserving.

Insurers record detailed information related to claims (e.g. the cause of the claim) and policies (e.g. the value of the insured risk) for pricing insurance contracts. However, this information is largely neglected when estimating the reserve for future liabilities originating from past exposures. We present a flexible, yet highly interpretable framework for including these claim and policy-specific covariates in a reserving model. Our framework focuses on three building blocks in the development process of a claim: the time to settlement, the number of payments and the size of each payment. We carefully choose a generalized linear model (GLM) to model each of these stochastic building blocks in discrete time. Since GLMs are applied in the pricing of insurance contracts, our project bridges the gap between pricing and reserving methodology. We propose model selection techniques for GLMs adapted for censored data to select the relevant covariates in these models and demonstrate how the selected covariates determine the granularity of our reserving model. At one extreme, including many covariates captures the heterogeneity in the development process of individual claims, while at the other extreme, including no covariates corresponds to specifying a model for data aggregated in two-dimensional contingency tables, similar to the run-off triangles traditionally used by reserving actuaries. The set of selected covariates then naturally determines the position the actuary should take in between those two extremes. We illustrate our method with case studies on real life insurance data sets. These case studies provide new insights in the covariates driving the development of claims and demonstrate the accuracy and robustness of the reserving methodology over time.