An empirical Bayesian and Buhlmann approach with non-homogenous Poisson process

All general insurance companies in Indonesia have to adjust their current premium rates according to maximum and minimum limit rates in the new regulation established by the Financial Services Authority (Otoritas Jasa Keuangan / OJK). In this research, we estimated premium rate by means of the Bayesian and the Buhlmann approach using historical claim frequency and claim severity in a five-group risk. We assumed a Poisson distributed claim frequency and a Normal distributed claim severity. Particularly, we used a non-homogenous Poisson process for estimating the parameters of claim frequency. We found that estimated premium rates are higher than the actual current rate. Regarding to the OJK upper and lower limit rates, the estimates among the five-group risk are varied; some are in the interval and some are out of the interval.