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.