Forecasting aggregate claims using score‐driven time series models

In the insurance industry, premium estimation and ruin probability valuation depend fundamentally on the aggregate claims distribution. From the mathematical point of view, the aggregated claims variable is a random sum of random variables. Obtaining the analytical expression for its probability distribution is a hard task. In this paper, a new approach is proposed for the modeling of the aggregated claims predictive distribution. The newly proposed generalized autoregressive score models are combined to specify non‐Gaussian distributions for both the number of claims and the claims severity. In all models, appropriate parameters were made time varying according to a score‐driving mechanism. By the use of the fast Fourier transform, we are then able to numerically obtain the aggregated claims distribution. The proposed method is applied to real data, provided by a Brazilian motor insurer.