Combined modelling of micro-level outstanding claim counts and individual claim frequencies in non-life insurance

Usually, the actuarial problems of predicting the number of claims incurred but not reported (IBNR) and of modelling claim frequencies are treated successively by insurance companies. New micro-level methods designed for large datasets are proposed that address the two problems simultaneously. The methods are based on an elaborated occurrence process model that includes both a claim intensity model and a claim development model. The influence of claim feature variables is modelled by suitable neural networks. Extensive simulation experiments and a case study on a large real data set from a motor legal insurance portfolio show accurate predictions at both the aggregate and individual policy level, as well as appropriate fitted models for claim frequencies. Moreover, a novel alternative approach combining data from classic triangle-based methods with a micro-level intensity model is introduced and compared to the full micro-level approach.