Constrained Forecasting of the Number of IBNR Claims

We consider the problem of forecasting the number of claims incurred. After subtracting the number of claims reported to date, the number of claims incurred but not reported (IBNR) can be forecasted. The basic model assumes that the number of claims per accident period follows an autoregressive moving average time series process. Instead of assuming the data reavailable in the usual claim run-off triangle format, we assume that the only data available are the number of claims reported at the valuation date for each accident interval of an observation period. Box-Jenkins methods are used to forecast the ultimate number of claims incurred and to obtain approximate confidence intervals for the number of claims incurred. The forecast of the ultimate number of claims incurred is used to derive the IBNR forecast. We show how additional information on the number of claims reported by the valuation date can be incorporated in the model when the process is autoregressive.