A time change strategy to model reporting delay dynamics in claims reserving

This paper considers the problem of predicting the number of claims that have already incurred in past exposure years, but which have not yet been reported to the insurer. This is an important building block in the risk management strategy of an insurer since the company should be able to fulfill its liabilities with respect to such claims. Our approach puts emphasis on modeling the time between the occurrence and reporting of claims, the so-called reporting delay. Using data at a daily level we propose a micro-level model for the heterogeneity in reporting delay caused by calendar day effects in the reporting process, such as the weekday pattern and holidays. A simulation study identifies the strengths and weaknesses of our approach in several scenarios compared to traditional methods to predict the number of incurred but not reported claims from aggregated data (i.e. the chain ladder method). We also illustrate our model on a European general liability insurance data set and conclude that the granular approach compared to the chain ladder method is more robust with respect to volatility in the occurrence process. Our framework can be extended to other predictive problems where interest goes to events that incurred in the past but which are subject to an observation delay (e.g. the number of infections during an epidemic).