Before revision: This paper considers the problem of predicting the number of claims that have already incurred in past exposure years , but which have not yet been reported to the insurer. This is an important building block in the risk management strategy of an insurer since the company should be able to fulfill its liabilities with respect to such claims .
After revision: This paper considers the problem of predicting the number of claims that have already incurred in past exposure years , but which are not yet observed due to a delay. Such delayed events are relevant in predicting the future cost of warranties, pricing maintenance contracts, determining the number of unreported claims in insurance and in modeling the outbreak of diseases. Disregarding these unobserved events results in a systematic underestimation of the event occurrence process.