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

TL;DR

This paper presents a novel machine learning framework using survival analysis techniques to forecast IBNR claim frequencies, integrating individual claim features and hazard function estimation methods.

Contribution

It introduces a new approach combining survival analysis with machine learning models for IBNR frequency prediction, ensuring coherence across different time granularities.

Findings

The methods outperform traditional models in simulations.

The approach is effective on real-world data.

Machine learning models provide flexible hazard function estimation.

Abstract

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 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.