Computing credibility bonus-malus premiums using the total claim amount distribution

Abstract

Assuming a bivariate prior distribution for the two risk parameters appearing in the distribution of the total claim amount when the primary distribution is geometric and the secondary one is exponential, we derive Bayesian premiums which can be written as credibility formulas. These expressions can be used to compute bonus-malus premiums based on the distribution of the total claim amount but not for the claims which produce the amounts. The methodology proposed is easy to perform, and the maximum likelihood method is used to compute the bonus-malus premiums for a real set of automobile insurance data, one that is well known in actuarial literature.