  A Bonus-Malus System (BMS) in insurance is a premium adjustment mechanism
widely used in a posteriori ratemaking process to set the premium for the next
contract period based on a policyholder's claim history. The current practice
in BMS implementation relies on the assumption of independence between claim
frequency and severity, despite the fact that a series of recent studies report
evidence of a significant frequency-severity relationship, particularly in
automobile insurance. To address this discrepancy, we propose a copula-based
correlated random effects model to accommodate the dependence between claim
frequency and severity, and further illustrate how to incorporate such
dependence into the current BMS. We derive analytical solutions to the optimal
relativities under the proposed framework and provide numerical experiments
based on real data analysis to assess the effect of frequency-severity
dependence in BMS ratemaking.
