Insurance Premium Prediction via Gradient Tree-Boosted Tweedie Compound Poisson Models

TL;DR

This paper introduces a gradient tree-boosting approach for Tweedie compound Poisson models, enabling flexible, nonlinear insurance premium predictions that outperform traditional linear models, with practical implementation in an R package.

Contribution

It presents a novel gradient boosting algorithm for Tweedie models, allowing nonlinear modeling and complex predictor interactions in insurance premium prediction.

Findings

The method achieves superior prediction accuracy in simulations.

It outperforms existing methods on auto insurance claim data.

The R package facilitates easy application and interpretation.

Abstract

The Tweedie GLM is a widely used method for predicting insurance premiums. However, the structure of the logarithmic mean is restricted to a linear form in the Tweedie GLM, which can be too rigid for many applications. As a better alternative, we propose a gradient tree-boosting algorithm and apply it to Tweedie compound Poisson models for pure premiums. We use a profile likelihood approach to estimate the index and dispersion parameters. Our method is capable of fitting a flexible nonlinear Tweedie model and capturing complex interactions among predictors. A simulation study confirms the excellent prediction performance of our method. As an application, we apply our method to an auto insurance claim data and show that the new method is superior to the existing methods in the sense that it generates more accurate premium predictions, thus helping solve the adverse selection issue. We have implemented our method in a user-friendly R package that also includes a nice visualization tool for interpreting the fitted model.