Description: The minimum distance estimator proposed allows for the selection of the best fitting family member without prior distributional assumptions. It is shown that this estimator is consistent and can be made either robust or asymptotically efficient. Its asymptotic distribution is derived and and illustrated with automobile insurance data. From the Actuarial Research Clearing House 1990 Vol. 1

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: Several authors have used Fourier inversion to compute prices of puts and calls, some using Parseval’s theorem. The expected value of max[S K,0] also arises in excess-of-loss of stop-loss insurance. This is the abstract of a paper that shows that Fourier methods may be used to compute them. The authors take the idea of using Parseval’s theorem further: 1. formulas requiring weaker assumptions, 2. relationship with classical inversion theorems for probability distributions, 3. formulas for pay-offs which occur in insurance. Numerical examples are provided.

Description: This is a presentation from 43rd Actuarial Research Conference ARC, Regina, August 14–16, 2008. This talk will present the moment generating function of the discounted compound Poisson aggregate sums when the deflated claims are PH distributed and moment generating function of the discounted compound renewal sums.

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 'A Stochastic Definition of Future Shares'. The traditional definition of actuarial future values and stochastic definition of Ramsay are discussed. A modification of Ramsay's definition is proposed and an application to life insurance reserves is presented.

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.

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.