Yi Yang (McGill University)

New Techniques for Modeling Non-life Insurance Claims

Tweedie’s Compound Poisson model is a popular method to model data with probability mass at zero and non-negative, highly right-skewed distribution. Motivated by wide applications of the Tweedie model in various fields such as actuarial science, we investigate a grouped elastic net method and a boosted nonparametric method for the Tweedie model in the context of the generalized linear model. For the grouped elastic net method, in order to efficiently compute the estimation coefficients, we devise a two-layer algorithm that embeds the blockwise majorization descent method into an iteratively re-weighted least square strategy. In together with the strong rule, the proposed algorithm is implemented in an easy-to-use R package HDtweedie, and is shown to compute the whole solution path very efficiently. On the other hand, the linear form of the logarithmic mean in the Tweedie GLM sometimes can be too rigid for many applications. As a better alternative, we propose a boosted nonparametric Tweedie model for pure premiums and use a profile likelihood approach to estimate the index and dispersion parameters. To our knowledge, there is no existing nonparametric Tweedie method available before this work. Our method is capable of fitting a flexible nonlinear Tweedie model and capturing complex interactions among predictors. We have also implemented this method in a user-friendly R package that includes a nice visualization tool for interpreting the fitted model.