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 is the abstract of the paper Minimum Quadratic Distance Estimators for the Zeta Parametric Family. In this paper, we propose a new estimator, based on quadratic distance, asymptotically fully efficient for parameter values greater than 2 and highly efficient for smaller values, but computationally more appealing than the maximum likelihood estimator we compare its asymptotic variance with that of the moment estimator and an estimator proposed by Seal, based on the ratio of the observed frequencies of the first two classes. We also discuss a goodness-of-fit test and a test to discriminate between the zeta distribution and the Poisson distribution truncated at 0.