Using Generalized Linear Models to Develop Loss Triangles in Reserving

The use of generalized linear models in loss reserving is not new; many statistical models have been developed to fit the loss data gathered by various insurance companies. The most popular models belong to what Glen Barnett and Ben Zehnwirth in "Best Estimates for Reserves" call the "extended link ratio family (ELRF)," as they are developed from the chain ladder algorithm used by actuaries to estimate unpaid claims. Although these models are intuitive and easy to implement, they are nevertheless flawed because many of the assumptions behind the models do not hold true when fitted with real-world data. Even more problematically, the ELRF cannot account for environmental changes like inflation which are often observed in the status quo. Barnett and Zehnwirth conclude that a new set of models that contain parameters for not only accident year and development period trends but also payment year trends would be a more accurate predictor of loss development. This research applies the paper's ideas to data gathered by Company XYZ. The data was fitted with an adapted version of Barnett and Zehnwirth's new model in R, and a trend selection algorithm was developed to accompany the regression code. The final forecasts were compared to Company XYZ's booked reserves to evaluate the predictive power of the model.