Bonus-malus in insurance portfolios

This thesis constitutes a research work on Bonus-Malus (BM) systems in insurance portfolios, featuring designing pricing strategies and examining associated solvency risks. The first piece of work proposed two different pricing models via the Bayesian approach. Results imply adverse attitudes towards policyholders having a history of many small claims, when the modelling for claim severities takes different forms. On the other hand, the rest of the work dedicated to embedding a BM structure under a risk analysis framework, where the focus lies in measuring the underlying ruin probabilities. It was necessary to initially investigate a discrete model where such probability could be obtained through recursions. As for a continuous model, BM feature was reflected by a Bayesian estimator for premium adjustment. Such construction normally brings in a dependence structure to the risk model thus violating classical assumptions. One way was to inspect how different it is from a classical risk model. Then through some conditional arguments one could find accordingly a solution based on results in literature. From another perspective, it has been found that for a No Claim Discount (NCD) or a Bonus system, an alteration in premium rates could be transformed equivalently to an interchange of distribution between inter-claim times. Then some Markov properties were able to be diagnosed under higher dimensions, which leads to a further possibility of computations. Results can be found in the form of simulations