# Statistical Models in Actuarial Science

Statistical Models in Actuarial Science
Organizer and Chair: Jean-Philippe Boucher (UQAM)
[PDF]

MATHIEU PIGEON, UQAM
Macro and Micro Methods in Non-Life Claims Reserving  [PDF]

Traditional methods for loss reserving in non-life insurance (Chain-Ladder, Bornhuetter Ferguson, London Chain, etc.) are constructed for aggregated data. Progress over the past decades in computing resources and greater availability of individual statistical data have resulted in the development of new models for individual dataset. In this talk, we will analyze the impacts of both approaches (macro and micro, respectively) on the evaluation of the reserve risk based on some parametric models (Poisson regression, quasi-Poisson regression, etc.) and generalized method of moments estimators. Results will be illustrated with simulations and a dataset from the industry.
PENG SHI, University of Wisconsin
A Pair Copula Construction Model for Insurance Experience Rating  [PDF]

In non-life insurance, insurers use experience rating to adjust premium to reflect the policyholder's previous claim experience. Performing prospective experience rating can be challenging when the claim distribution is complex. In this article, we introduce a mixed vine pair copula construction framework for modeling semicontinuous longitudinal claims. Specifically, a two-component mixture regression is employed to accommodate the zero inflation and thick tails in claim distribution. The temporal dependence among repeated observations is modeled using a sequence of bivariate conditional copulas based on a mixed D-vine. In the application of government property insurance from the state of Wisconsin, we show that the proposed approach offers substantial opportunities for separating risks and identifying profitable business when compared with alternative experience rating methods.
CARY CHI-LIANG TSAI, Simon Fraser University
Applications of the Bühlmann Credibility Model to Mortality Forecasting  [PDF]

In this presentation, we first propose the Bühlmann credibility model to forecast mortality rates, and then compare forecasting performances between the proposed Bühlmann model and some leading mortality models. Empirical results based on mortality data for both genders of some country, a wide range of fitting year spans, and three forecasting periods show that the Bühlmann credibility model contributes to much better forecasting performances measured by the MAPE (mean absolute percentage error). Moreover, we give meaningful credibility interpretations regarding the decrement rates of an individual time trend for age $x$ and a group time trend for all ages, and discuss the effects of the slope and intercept of the linear functions for the forecasted mortality rates under the underlying models.