Prediction of the Ultimate Claims Based on Cumulative Payments and Claims-Incurred Data Using Kalman-Filter Theory

One of the main tasks in non-life insurance is the prediction of outstanding loss liabilities for run-off portfolios. Additionally, the quantification of the prediction uncertainty is also of great interest. In this paper we look at this actuarial problem in a bivariate framework, i.e. we assume that we have two different sources of information, namely a paid and an incurred run-off portfolio. Based on these two information sources we derive a formula for the ultimate claim and for the mean-square-error of prediction (MSEP) using Kalman-filter techniques. Finally, an example for a given triangle pair (paid-incurred-triangle data) is presented