BAYESIAN CONFIDENCE INTERVALS FOR THE NUMBER AND THE SIZE OF LOSSES IN THE OPTIMAL BONUS–MALUS SYSTEM.

Most of the so far proposed Bonus–Malus Systems (BMSs) establish a premium only according to the number of accidents, without paying attention to the vehicle damage severity. [Frangos and Vrontos 2001] proposed the optimal BMS design based not only on the number of accidents of a policyholder, but also on the size of loss of each accident. In our work, we apply the approach presented by Frangos and Vrontos to construct the Bayesian confidence intervals for both the number of accidents and the amount of damage caused by these accidents. We also conduct some simulations in order to create tables of estimates for both the numbers and the sizes of losses and to compute the realizations of the corresponding Bayesian confidence intervals. We compare the results obtained by using our simulation studies with the appropriate results derived through an application of an asymmetric loss function and its certain modification.