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A General Approach to Buhlmann Credibility Theory

Credibility theory is widely used in insurance. It is included in the examination of the Society of Actuaries and in the construction and evaluation of actuarial models. In particular, the Buhlmann credibility model has played a fundamental role in both actuarial theory and practice. It provides a mathematical rigorous procedure for deciding how much credibility should be given to the actual experience rating of an individual risk relative to the manual rating common to a particular class of risks. However, for any selected risk, the Buhlmann model assumes that the outcome random variables in both experience periods and future periods are independent and identically distributed. In addition, the Buhlmann method uses sample mean-based estimators to insure the selected risk, which may be a poor estimator of future costs if only a few observations of past events (costs) are available. We present an extension of the Buhlmann model and propose a general method based on a linear combination of both robust and efficient estimators in a dependence framework. The performance of the proposed procedure is demonstrated by Monte Carlo simulations.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc1011812
Date08 1900
CreatorsYan, Yujie yy
ContributorsSong, Kai-Sheng, Allaart, Pieter C., Quintanilla, John
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatv, 90 pages, Text
RightsPublic, Yan, Yujie yy, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved.

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