The credibility premiums based on estimated moment-generating function

Traditionally, experience ratemaking is in principle based on the idea of Bühlmann’s credibility theory that, except for net premiums, was rarely applied to other premium calculation principles. This article uses Bühlmann’s credibility procedure to estimate moment-generating functions (MGFs) of risks and then deduces estimates of moments of those risks. For the premium calculation principles that can be expressed as functions of certain moments or more directly of the MGFs, this article develops a new type of experience ratemaking methods by means of the estimated MGFs and discusses their consistency and asymptotic normality. Numerical simulation shows that, under the Esscher and exponential premium principles, the new credibility estimates are better than existing credibilityestimates in the literature.