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Bayesian credibility premium with GB2 copulas

Author

Listed:
  • Jeong Himchan

    (Department of Statistics and Actuarial Science, Simon Fraser University)

  • Valdez Emiliano A.

    (Department of Mathematics, University of Connecticut)

Abstract

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.

Suggested Citation

  • Jeong Himchan & Valdez Emiliano A., 2020. "Bayesian credibility premium with GB2 copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 157-171, January.
    • Handle: RePEc:vrs:demode:v:8:y:2020:i:1:p:157-171:n:22
    DOI: 10.1515/demo-2020-0009
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    References listed on IDEAS

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    1. McDonald, James B. & Butler, Richard J., 1990. "Regression models for positive random variables," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 227-251.
    2. Yang, Xipei & Frees, Edward W. & Zhang, Zhengjun, 2011. "A generalized beta copula with applications in modeling multivariate long-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 265-284, September.
    3. Jewell, William S., 1974. "Credible Means are exact Bayesian for Exponential Families," ASTIN Bulletin, Cambridge University Press, vol. 8(1), pages 77-90, September.
    4. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
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    Cited by:

    1. Jeong, Himchan & Valdez, Emiliano A., 2020. "Predictive compound risk models with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 182-195.

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