Journal of East China Normal University(Natural Sc ›› 2010, Vol. 2010 ›› Issue (6): 156-168.

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Multidimensional credibility models with random common effects

ZHANG Yi1, WEN Li-min 1,2   

  1. 1. Institute of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China; 2. School of Finance and Statistics, East China Normal University, Shanghai 200241, China
  • Received:2009-12-01 Revised:2010-03-01 Online:2010-11-25 Published:2010-11-25
  • Contact: WEN Li-min

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Abstract: Multidimensional credibility models with a random common effect were built, and the inhomogeneous and homogeneous credibility estimators were derived. Further, some properties of these estimators were presented. Analogy to the classical credibility theory, the multidimensional credibility estimators with the common effect can also be expressed as the weighted sum of individual mean, collective mean and collective premium, where these weights are so-called credibility factor matrices. Finally, a numerical example
was given to show the calculations of multidimensional credibility estimators.

Key words: random common effect, multidimensional credibility, orthogonal projection. , credibility premium, random common effect, multidimensional credibility, orthogonal projection.

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