Estimation of the Credibility in the Original Bühlmann Model Illustrated by Introducing a Regression Technique

Abstract

In this article we give the mathematical theory of some credibility models. The first section describes the original credibility model of Bühlmann and we derive the best linearized credibility estimator for this model. His original model, involving only one contract, contains the basics of all further credibility models. Section 2 contains a description of the Hachemeister regression model allowing for effects like inflation.

Keywords

• linearized regression credibility premium
• the original credibility model of Bühlmann