Accession Number : ADA328061
Title : Three Papers in Credibility Theory: The Use of Collateral Data in Credibility Theory: A Hierarchical Model; Bayesian Regression and Credibility Theory; Bayesian Inverse Regression and Discrimination: An Application of Credibility Theory.
Descriptive Note : Research rept.,
Corporate Author : CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
Personal Author(s) : Jewell, William S. ; Avenhaus, Rudolph
PDF Url : ADA328061
Report Date : JUN 1976
Pagination or Media Count : 99
Abstract : In classical credibility theory, a linearized Bayesian forecast of the fair premium for an individual risk contract is made using prior estimates of the collective fair premium and individual experience data. However, collateral data from other contracts in the same portfolio is not used, in spite of intuitive feelings that this data would contain additional evidence about the quality of the risk collective from which the portfolio was drawn. By using a hierarchical model, one makes the individual risk parameters exchangeable, in the sense of de Finetti, and a modified credibility formula is obtained which uses the collateral data in an intuitively satisfying manner. The homogeneous formula of Buhlmann and Straub is obtained as a limiting case when the hyperprior distribution becomes 'diffuse'.
Descriptors : *BAYES THEOREM, *STATISTICAL DECISION THEORY, MATHEMATICAL MODELS, CONTRACTS, PARAMETERS, FORECASTING, REGRESSION ANALYSIS, QUALITY, LINEARITY, INVERSION, HIERARCHIES, HOMOGENEITY.
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE