Abstract

This thesis presents an intuitive way to do predictive modeling in actuarial science. Generalized Linear Models (GLMs) are the standard tool for predictive modeling in the actuarial literature and in actuarial practice, yet GLMs can be quite restrictive. The aim of this work is to model claims and to propose solutions to current actuarial problems such as high variability in large data-sets, variable selection, overfitting, dealing with highly correlated variables and detecting non-linear effects such as interactions.

Regularization techniques are crucial for modeling big data, which means dealing with high-dimensionality, sometimes noisy data that often contains many irrelevant predictors. Penalized regression is a set of regression techniques that impose a constraint/penalty on the regression coefficients and can be used as a powerful variable selection tool as well. They are a generalization of GLMs and include techniques such as Ridge regression, lasso, group-lasso and Elastic Net. The proposed approach is a hierarchical group-lasso-type model that can efficiently handle variable selection and interaction detection between variables while enforcing strong hierarchy. This is achieved by imposing a penalty on the coefficients at the individual and group level. By optimizing the penalized objective function the model performs variable selection and estimation. Additionally, the model automatically detects interactions which is another important factor to achieve a high predictive power. For those purposes the group-lasso method is investigated for the Poisson and gamma distributions to perform frequency-severity modeling.