Description: This research was funded by the Natural Sciences and Engineering Research Council of Canada [NSERC] Discovery Grant 36860–06. Loss reserving is one of the most challenging tasks facing actuaries. Numerous approaches have been developed to give reasonable estimates. Generalized linear models [GLMs] are becoming quickly popular statistical analysis methods to estimate loss reserves. However, most of these models are aggregate reserving methods based on loss development triangles, without using information with regard to the actual claims processes. This paper establishes a more sophisticated structural reserving method incorporating more detailed information, such as the premium exposure emergence pattern, the loss emergence pattern and the loss development pattern, within the framework of GLMs.

Description: This paper derives limited fluctuations credibility results for the Generalized Linear Model GLM and the extended case of generalized linear mixed model GLMM. It shows how credibility depends on the sample size, the distribution of covariates, and the link function. This provides a mechanism to obtain confidence intervals for the GLM and GLMM estimators.