IBNR claims reserving using INAR processes
The reserving problem for incurred but not reported (IBNR) claims is of great importance to the non-life insurers. A lot of sophisticated methods and suitable models have been discussed widely in both academia and industry. These models are generally either non-parametric or parametric. Although the classical non-parametric models, such as chain-ladder method and Bornhuetter-Freguson method, have been accepted greatly, parametric models under stochastic frameworks have drawn more and more attention. As the rationale of frequency-severity techniques has been justified, more models for claim counts have been developed. Kremer (1995) proposed an idea of modeling IBNR claim counts using the integer-valued autoregressive (INAR) processes. In this project, we extend Kremer’s idea of studying claims reserving problem by proposing a new INAR process to model the unclosed claims. The properties, estimation methods and prediction of the proposed model are discussed. The effectiveness of different estimation methods is discussed in the numerical illustrations.