For observations over a period of time, Bayesian credibility premium may be used to predict the value of a response variable for a subject, given previously observed values. In this article, we formulate Bayesian credibility premium under a change of probability measure within the copula framework. Such reformulation is demonstrated using the multivariate generalized beta of the second kind (GB2) distribution. Within this family of GB2 copulas, we are able to derive explicit form of Bayesian credibility premium. Numerical illustrations show the application of these estimators in determining experience-rated insurance premium. We consider generalized Pareto as a special case.
 Bailey, A. L. (1950). Credibility procedures: Laplace’s generalization of Bayes’ rule and the combination of collateral knowledge with observed data. Proceeding of the Casualty Actuarial Society 37(67), pp. 7–23.Search in Google Scholar
 Bühlmann, H. and A. Gisler (2005). A Course in Credibility Theory and its Applications. Springer, Berlin.Search in Google Scholar
 Hougaard, P., B. Harvald, and N. V. Holm (1992). Measuring the similarities between the lifetimes of adult danish twins born between 1881–1930. J. Amer. Statist. Assoc. 87(417), 17–24.Search in Google Scholar
 Joe, H. (1997). Multivariate Models and Multivariate Dependence Concepts. Chapman and Hall, London.Search in Google Scholar
 Mayerson, A. L. (1964). A bayesian view of credibility. Proceeding of the Casualty Actuarial Society 51(95), pp. 85–104.Search in Google Scholar
 Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, 229–231.Search in Google Scholar
 Yang, X., E. W. Frees, and Z. Zhang (2011). A generalized beta copula with applications in modeling multivariate long-tailed data. Insurance Math. Econom. 49(2), 265–284.10.1016/j.insmatheco.2011.04.007Search in Google Scholar
© 2020 Himchan Jeong et al., published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.