| It is an important work to establish scientific premium calculation principles and methods in nonlife actuarial science. Under quadratic loss principle, Bayes premium is the best. However, the prior density function must be known when we use Bayes for-mula, which is difficult in reality. Hence the main method to solve this kind of question is to estimate the individual premium with history data. When the estimator is restricted in the field of linear function of history data, the premium is called credibility premium. Though credibility premium is easy to be calculated, its disadvantages also exist. Since it is linear approximation to individual premium, its ASEL(Average Squared Error Loss) would not be less than the ASEL of Bayes premium. Besides, credibility theory is limited to calculate pure premium only. But for an insurer who gain pure premium will go bankruptcy with probability 1.The major work of this paper is to find an empirical Bayes estimator of individual premium to avoid the disadvantages of Bayes and credibility method.This paper contains 4 chapters. The 1st chapter introduces the background and its current situation and prospect, with a brief introduction to empirical Bayes method. In the 2nd chapter empirical premium formulas both in Buhlmann and Biihlmann-Straub model are proposed. In the 3rd chapter similar formulas are proposed under exponential premium principle and any principle whose first and second moments are exist. The 4th chapter is the simulation part of the empirical Bayes estimators. |
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