Bonus–malus system using an exponential loss function with an Inverse Gaussian distribution

In most companies, the importance of the auto-insurance has prompted their actuaries to look for different tariff systems that distribute the exact weight of each risk among portfolios. The use of quadratic loss functions in most of classical bonus–malus systems leads to very high maluses. To avoid this problem, we use an exponential loss function and subsequently obtain the result for the Poisson–Inverse Gaussian model. We show, with a numerical example, that this new model fits better than the classical one for our data. Furthermore, it provides maluses that not so high, as well as other advantages for actuaries.