A Credibility Model with Random Fluctuations In Delay Probabilities for the Prediction of IBNR Claims

We consider a general credibility model for the prediction of IBNR-claims which allows for random fluctuations m the underlying delay distribution. Such fluctuations always bring about decreasing credibility It is shown that even negative credibility is achieved for more substantial fluctuations m the delay distribution. Special attention ~s paid to the mixed Poisson case for claim numbers including the discussion of parameter estimation.

Keywords Credibility theory; IBNR-reserve; delay distribution; Dirichlet distribution; linear sufficiency