Bayesian tree models with applications to Insurance ratemaking

We are looking for strong candidates to work on this exciting project described below!

An insurance portfolio offers protection against a specified type of risk to a collection of policyholders with various risk profiles. Insurance companies differentiate premiums to reflect the heterogeneity of risks in their portfolio. Insurance companies use risk factors to group policyholders with similar risk profiles in tariff classes. Premiums are equal for policyholders within the same tariff class and should reflect the inherent riskiness of each class. The process of constructing these tariff classes is also known as risk classification. Pricing (or ratemaking) through detailed risk classification is the mechanism for insurance companies to compete and to reduce the cost of insurance contracts. A risk classification system should not only allow insurers to discriminate their products in a fair and equitable manner, but should also be constructed based on a sound statistical basis.

Generalized linear models (GLMs) are nowadays standard industry practice for pricing risks. Many extensions of GLMs, such as, regularized GLMs and GAMs, GLMMs, have also been discussed in the literature. New actuarial methods inspired from recent progress in machine learning (ML), such as tree-based methods and variations, offer the potential to revolutionize how insurance premiums are computed. These methods could enable actuaries to propose models that are both fairer and more accurate. 

One of the goals of this project is to explore a combined GLMs and Bayesian treed models (e.g., Bayesian CART) for insurance ratemaking. Some key questions to be explored include feature selection, choice of loss functions, class-imbalance problem for insurance data, model stability, and interpretability. The Bayesian tree models are known to work very well for many types of real-life data but the underlying theory is still to be understood by researchers. Another goal of this project is to try to understand the mechanism of the method from a theoretical point of view.