Topics in high dimensional statistical learning with applications in property-casualty insurance

In this thesis, we develop new methods instrumental for claim severity analysis with big data in property-casualty insurance. The challenge arises from the ubiquity of huge claims in property-casualty insurance claim data, which generally invalidates the predictive efficacy of existing machine learning techniques. We propose a new method to select features for predicting excess loss over a certain threshold, with heavy-tailed loss data. Additionally, we propose new classification method and use it to classify claims with a high risk of severe losses. The developed techniques are fused in a real application using commercial automobile insurance claim data. The application reveals novel business insights on property-casualty insurance ratemaking and shows an improvement of our method over two commonly used claim severity models.