A Financially Balanced Bonus/Malus System

The premiums for a bonus-malus system which stays in financial equilibrium over the yeats are calculated This is done by minimalizing a quadratic function of the difference between the premium for an optimal BMS with an infinite number of classes and the premium for a BMS with a finite number of classes, weighted by the stationary probability of being in a certain class, and by transposing various constraints on the system,