  Bonus-Malus Systems traditionally consider a customer's number of claims
irrespective of their sizes, even though these components are dependent in
practice. We propose a novel joint experience rating approach based on latent
Markovian risk profiles to allow for a positive or negative individual
frequency-severity dependence. The latent profiles evolve over time in a Hidden
Markov Model to capture updates in a customer's claims experience, making claim
counts and sizes conditionally independent. We show that the resulting risk
premia lead to a dynamic, claims experience-weighted mixture of standard
credibility premia. The proposed approach is applied to a Dutch automobile
insurance portfolio and identifies customer risk profiles with distinctive
claiming behavior. These profiles, in turn, enable us to better distinguish
between customer risks.
