Ratemaking: Advanced Techniques and GLM Applications

GLM-Based Ratemaking

Modern ratemaking uses GLMs to model frequency and severity separately. Claim frequency is modeled with Poisson or negative binomial regression using a log link, with exposure as an offset: ln(E[N_i]) = ln(w_i) + x_i'*beta. Claim severity uses Gamma or inverse Gaussian regression with a log link: ln(E[X_i|X_i>0]) = x_i'*gamma. The pure premium is the product of predicted frequency and predicted severity. This multiplicative structure allows rating factors to be applied independently across dimensions.

Advanced Techniques

Regularization (ridge and lasso) handles multicollinearity and performs variable selection. Elastic net combines both penalties. Interaction terms capture dependencies between rating variables (e.g., age and vehicle type). Smoothing splines or restricted cubic splines model nonlinear effects of continuous variables within the GLM framework. Territorial rating uses spatial smoothing or credibility adjustments. Transition rules manage premium dislocation when implementing new rating algorithms. Exam MAS-II tests the full GLM ratemaking pipeline: model specification, estimation, diagnostics, relativities extraction, and implementation considerations including off-balance and capping.