The Maximum Entropy Method to the Credibility Estimation

Besides the claims data in the past, certain assumptions about the distribution of claimsare required to derive the credibility premium in the classical theory. In the paper, the credibility premium can be calculated via the maximum entropy method if we know nothing about the distribution of claims . Furthermore, two corollaries are obtained under certain assumptions, that is, new claims have more weight than the old ones and the classical credibility formula is a special case of the credibility premium derived in the present paper. Finally, the simulation study is presented to illustrate that the credibility premium in the present paper is better than other models if the mean square error is taken as the evaluation criterion.