Bonus-malus and ruin probabilities

What is it about?

The probability of ruin, in continuous and finite time, is numerically evaluated under the classical Cramer-Lundberg risk process framework for a large motor insurance portfolio, where we allow for a posteriori premium adjustments, according to the claim record of each individual policyholder. We propose that the probability of ruin can be interpreted as a measure to decide between different bonus-malus scales or between different bonus-malus rules. In our work the required initial surplus can also be evaluated.

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Why is it important?

The evaluation of finite time ruin probabilities in finite time for a motor insurance portfolio with posterior ratemaking and based on a classical Markov bonus-malus system is unique. Ruin probabilities in this way can be viewed as a short or medium time evalution mesasure for bonus-malus ssystems.