Determination of multiple period credibility premium on Bühlmann credibility model

Bühlmann credibility model generally used to predict premium tariff for each policyholder at (n+1)-th period based on n periods historical claims or also called one period model. In this paper, Bühlmann credibility model will able to predict more than one period or also called multiple period model. Multiple period model allows insurer to predict amount of premium not only one period ahead but also few periods ahead based on n periods historical claims. The model considers two important components, which are future claim and anticipating premium by giving weight for each component. To minimize the difference between multiple period premium and future claim also between multiple period premium and anticipating premium, quadratic programming problem is used on this paper. Quadratic programming problem is solved by Karush-Kuhn-Tucker conditions. By applying the concept of multiple period models to real data, it can be seen that the Bühlmann multiple period credibility model gives premiums more fair for each policyholder than using the one-period credibility model. By using this model, hopefully insurer enables to conduct long-term financial planning and increases effectiveness of work.