Credibility estimation of claim frequency

Credibility theory in insurance is essentially a form of experience-rating that attempts to use the data in hand as well as the experience of others in determining rates and premiums. Two types of data are used in the process of estimation using models based on the theory of credibility: data about own insurance risk and data about comparable insurance risks. The predictor for the next year‘s experience that is linear in the claims experience and optimal in the sense of least squares turns out to be a weighted average of the claims experience of the individual contract and the experience for the whole portfolio. The weight factor is the credibility attached to the individual experience, hence it is called the credibility factor, and the resulting premiums are called credibility premiums. In this article we review the Bühlmann-Straub model that is the most important credibility model and has a lot of application in non-life and life insurance as well as in reinsurance. The Bühlmann- -Straub model belongs to the greatest accuracy credibility theory. Credibility estimators produced by this approach are such linear Bayes estimators that minimize the mean squared error (MSE). Credibility estimators compared with Bayes estimators don‘t require the choice of a prior distribu- tion. Bühlmann showed that credibility estimators depend only on first and second moments that are easy to estimate from statistical data. This paper describes the technique of the credibility estimation for the claim frequency under assumptions of the Bühlmann-Straub model. The paper also includes the application of this credi- bility theory and techniques in third party motor vehicle insurance