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October  2009, 5(4): 893-910. doi: 10.3934/jimo.2009.5.893

The credibility premiums under generalized weighted loss functions

Limin Wen 1, , Xianyi Wu 1, and  Xiaobing Zhao 2,

1. 

Department of Statistics and Actuarial Science, East China Normal University, Shanghai, China, China
2. 

School of Science, Jiangnan University, Wuxi, Jiangsu, China

Received  August 2008 Revised  March 2009 Published  August 2009

In the classical credibility theory, almost all the credibility premium models are built on the basis of pure premium. However, the insurance practice demands that the premium must have a positive safety loading. In this paper, we consider the premium principle induced by a generalized loss function that can provide the premium principle with\ a positive safety loading. Under this generalized loss function, we derive its Bayes premium and two types of credibility premiums. Both credibility premiums are approximately convex combinations of the collective premium and some functions of the historical claims; while in a first case the function is linear in the historical claims and the corresponding credibility premium is not consistency, in the other one the function is taken as an empirical version of the individual premium and the corresponding credibility premium converges to the individual premium.
Keywords: safety loading., generalized weighted premium, credibility estimator, generalized weighted loss function, consistency.
Mathematics Subject Classification: Primary: 91B30, 62P05; Secondary: 91B8.
Citation: Limin Wen, Xianyi Wu, Xiaobing Zhao. The credibility premiums under generalized weighted loss functions. Journal of Industrial & Management Optimization, 2009, 5 (4) : 893-910. doi: 10.3934/jimo.2009.5.893
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