Micro-level stochastic loss reserving for general insurance

The vast literature on stochastic loss reserving concentrates on data aggregated in run-off triangles. However, a triangle is a summary of an underlying data set with the development of individual claims. We refer to this data set as ‘micro-level’ data. Using the framework of Position Dependent Marked Poisson Processes (as in Norberg (1993) and Norberg (1999)) and statistical tools for recurrent events
(as in Cook and Lawless (2007)), a data set is analyzed with liability claims from a European insurance company. We use detailed information of the time of occurrence of the claim, the delay between occurrence and reporting to the insurance company, the occurrences of payments and their sizes, and the final settlement. In contrast with the non-parametric Bayesian approach of Haastrup and Arjas (1996) our specifications are (semi)parametric and our approach is likelihood based. We
calibrate the model to historical data and use it to project the future development of open claims. An out-of-sample prediction exercise shows that we obtain detailed and valuable reserve calculations. For the case study developed in this paper, the micro-level model outperforms the results obtained with traditional loss reserving methods for aggregate data.