Title: A time change strategy to model reporting delay dynamics in claims reserving,
Abstract: 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).