**Authors:** Virginia Atanasiu

**Keywords:** The linear estimator, the Esscher premium, the variance premium.

### Abstract

In this paper we have obtained linear approximations which are unbiased estimates for the expected value part, respectively for the variance part and finally for the fluctuation part of the loading from the variance premium, using the greatest accuracy theory. The article provides a means to approximate the separate parts of the variance loaded premium by linear non-homogeneous credibility estimators. Apart from the purpose of this paper, which is to simply add "credibility" like estimators for the separate parts of the variance premium, we have presented some basic theorems
from statistics and some basic results on finding estimators with minimal mean squared error from probability theory. The fact that it is based on complicated mathematics, involving conditional expectations, needs not bother the user more than it does when he applies statistical tools like, discriminating analysis and scoring models.

Department of Mathematics

Academy of Economic Studies

Bucharest, Romania

E-mail:

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