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

Abstract

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.