Some Models of Bonus-Malus Optimal Systems

Some models of bonus-malus optimal systems are considered. The randomization principle is used as the basis of the model construction, that is to say, the supposition on the insurance portfolio uniformity is rejected which allows the conventional characteristics for the given contract to be calculated. Various bonus-malus systems are based on different models for a number of insurance payments according to insured accidents. Formulae to calculate model parameters using the method of moments are derived for the offered models. Numerical examples of calculation of bonus-malus optimal systems using the real data are given.