Regularization and Sparse Models in Insurance Pricing
How LASSO, Ridge, and Elastic Net regularization improve insurance pricing models on MAS-II.
Why Regularization Matters
Insurance pricing models with many rating variables risk overfitting, especially when some variables have limited credibility. Regularization adds a penalty term to the loss function that shrinks coefficient estimates toward zero, improving out-of-sample prediction. This is particularly relevant when working with high-dimensional data from telematics or text mining.
Methods and Applications
Ridge regression (L2 penalty) shrinks coefficients but retains all variables. LASSO (L1 penalty) performs automatic variable selection by driving some coefficients exactly to zero, producing sparse models. Elastic Net combines both penalties. For GLMs used in insurance pricing, regularization paths help identify which rating variables contribute meaningfully. The tuning parameter lambda controls the strength of regularization and is typically selected via cross-validation. On the exam, know how to interpret regularization paths, compare Ridge and LASSO behavior, and explain why sparse models can be preferable for regulatory and interpretability reasons.