Description: In the paper, the authors implement the empirical version of a robust Kalman filter credibility estimator with a data set, and compare its sensitivity to large claims with that of other credibility estimators in the literature.

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: In this paper some general properties of compound nonstationary Poisson processes are discussed as well as the possible shapes of the intensity function. A decomposition of the accumulated claims as a sum of independent compound Poisson sums is shown. An embedded discrete risk model is introduced. It is shown that ruin probabilities and maximal losses for the nonstationary risk model find lower bounds with the embedded discrete model. From Actuarial Research Clearing House 1994 VOL. 1.

Description: Two renewal processes, known in reliability maintenance as minimal repair and replacement policy, are introduced in this paper. Their properties are studied in the case where the generating random sequence has a distribution with periodic failure rate. Applications in risk theory are shown. From Actuarial Research Clearing House 1993, VOL. 1.

Description: In this article the authors work out the expected discounted penalty function for Levy processes. Unlike the classical compound Poisson case that models the individual claim size distribution and obtains from it the aggregate distribution, here the aggregate claims distribution is known. From Actuarial Research Clearing House, 2006.