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 is an abstract article on the distribution of discounted compound renewal sums.

Description: This is the abstract for the research on the application of discounted PH-renewal sums.

Description: This abstract describes a paper that shows how to calculate the distribution of discounted compound PH-renewal sums by inverting the Laplace transform.

Description: In an effort to build a bridge between epidemiological and actuarial modeling, this paper analyzes possible financial arrangements made against expenses resulted from medical treatments given to insured patients. Based on classical compartment models, the first part of this paper designs insurance policies for susceptible participants facing the risk of infection and formulates the financial obligations of both parties using actuarial methodology. For practical purposes, the second part employs a variety of numerical methods for calculating premiums and reserves. The last part illustrates the methods by designing insurance products for the Great Plague in Eyam and the SARS Epidemic in Hong Kong.

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: 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: 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.

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.