A machine learning approach based on survival analysis for IBNR frequencies in non-life reserving

We introduce new approaches for forecasting IBNR (Incurred But Not Reported) frequencies by leveraging individual claims data, which includes accident date, reporting delay, and possibly additional features for every reported claim. A key element of our proposal involves computing development factors, which may be influenced by both the accident date and other features. These development factors serve as the basis for predictions. While we assume close to continuous observations of accident date and reporting delay, the development factors can be expressed at any level of granularity, such as months, quarters, or year and predictions across different granularity levels exhibit coherence. The calculation of development factors relies on the estimation of a hazard function in reverse development time, and we present three distinct methods for estimating this function: the Cox proportional hazard model, a feed-forward neural network, and xgboost (eXtreme gradient boosting). In all three cases, estimation is based on the same partial likelihood that accommodates left truncation and ties in the data. While the first case is a semi-parametric model that assumes in parts a log linear structure, the two machine learning approaches only assume that the baseline and the other factors are multiplicatively separable. Through an extensive simulation study and real-world data application, our approach demonstrates promising results. This paper comes with an accompanying R-package, $\texttt{ReSurv}$, which can be accessed at \url{https://github.com/edhofman/ReSurv}