  A well-designed framework for risk classification and ratemaking in
automobile insurance is key to insurers' profitability and risk management,
while also ensuring that policyholders are charged a fair premium according to
their risk profile. In this paper, we propose to adapt a flexible regression
model, called the Mixed LRMoE, to the problem of a posteriori risk
classification and ratemaking, where policyholder-level random effects are
incorporated to better infer their risk profile reflected by the claim history.
We also develop a stochastic variational Expectation-Conditional-Maximization
algorithm for estimating model parameters and inferring the posterior
distribution of random effects, which is numerically efficient and scalable to
large insurance portfolios. We then apply the Mixed LRMoE model to a real,
multiyear automobile insurance dataset, where the proposed framework is shown
to offer better fit to data and produce posterior premium which accurately
reflects policyholders' claim history.
