Statistical modelling and forecasting of outstanding liabilities in non-life insurance

Non-life insurance companies need to build reserves to meet their claims liability cash flows. They often work with aggregated data. Recently it has been suggested that better statistical properties can be obtained when more aggregated data are available for statistical analysis than just the classical aggregated payments. When also the aggregated number of claims is available one can define a full statistical model of the nature of the number of claims, their delay until payment and the nature of these payments. In this paper we provide a new development in this direction by entering yet another set of aggregated data, namely the number of payments and when they occurred. A new element of our statistical analysis is that we are able to incorporate inflationary trends of payments in a direct and explicit way. Our new method is illustrated on a real life data set