1. The credibility premiums based on estimated moment-generating function
- Author
-
Guoping Mei, Jun Yu, Limin Wen, and Yi Zhang
- Subjects
Statistics and Probability ,050208 finance ,05 social sciences ,Strong consistency ,Asymptotic distribution ,Moment-generating function ,01 natural sciences ,Credibility theory ,Exponential function ,010104 statistics & probability ,Consistency (statistics) ,0502 economics and business ,Credibility ,Econometrics ,0101 mathematics ,Mathematics - Abstract
Traditionally, experience ratemaking is in principle based on the idea of Buhlmann’s credibility theory that, except for net premiums, was rarely applied to other premium calculation principles. This article uses Buhlmann’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.
- Published
- 2016