The Credibility Estimator with General Dependence Structure Over Risks

Abstract

In almost all credibility models considered previously, the claims are assumed to be independent over risks. However, from the practical point of view, it is not always the case, and hence, in this article, we investigate the credibility premiums when risks are allowed to be generally dependent. Firstly, we re-build the credibility estimators for Bühlmann and Bühlmann–Straub credibility models under general dependence structure over risks. The methods are then extended to the regression credibility models.

Keywords:

• Credibility premium
• Dependence
• Projection
• Regression credibility model

Mathematics Subject Classification:

• Primary 58F15, 58F17
• Secondary 53C35

Acknowledgments

The authors thank the following sources for their grants: the Science Foundation of Education Department of Jiangxi (New GJJ1046), Chinese NSF under No. 71001046 and Chinese NSF under No. 71001056.