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Bayesian credibility for GLMs

Title:

Bayesian credibility for GLMs

Garrido, José ORCID: https://orcid.org/0000-0002-2016-7524 and Xacur, Oscar Alberto Quijano (2018) Bayesian credibility for GLMs. Insurance: Mathematics and Economics . ISSN 01676687 (In Press)

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Official URL: http://dx.doi.org/10.1016/j.insmatheco.2018.05.001

Abstract

We revisit the classical credibility results of Jewell (1974) and Bühlmann (1967) to obtain credibility premiums for a GLM using a modern Bayesian approach. Here the prior distribution can be chosen without restrictions to be conjugate to the response distribution. It can even come from out–of–sample information if the actuary prefers.
Then we use the relative entropy between the “true” and the estimated models as a loss function, without restricting credibility premiums to be linear. A numerical illustration on real data shows the feasibility of the approach, now that computing power is cheap, and simulations software readily available.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Article
Refereed:Yes
Authors:Garrido, José and Xacur, Oscar Alberto Quijano
Journal or Publication:Insurance: Mathematics and Economics
Date:2018
Funders:
  • Natural Sciences and Engineering Research Council of Canada (NSERC)
Digital Object Identifier (DOI):10.1016/j.insmatheco.2018.05.001
ID Code:984212
Deposited By: ALINE SOREL
Deposited On:27 Aug 2018 16:36
Last Modified:14 Oct 2019 15:36

References:

Bernardo José M.. Intrinsic credible regions: An objective bayesian approach to interval estimation, TEST, 14 (2) (2005), pp. 317-384

Bühlmann H. Experience rating and credibility, Astin Bull., 4 (3) (1967), pp. 99-207

Daniels H.E. Exact saddlepoint approximations, Biometrika, 67 (1) (1980), pp. 59-63. URL http://biomet.oxfordjournals.org/content/67/1/59.abstract

de Jong P., Heller G.Z. Generalized Linear Models for Insurance Data, 9780511755408, Cambridge University Press (2008). URL http://dx.doi.org/10.1017/CBO9780511755408, Cambridge Books Online

De Vylder F.E. Non-linear regression in credibility theory, Insurance Math. Econom., 4 (3) (1985), pp. 163-172. URL http://EconPapers.repec.org/RePEc:eee:insuma:v:4:y:1985:i:3:p:163-172

Diaconis P., Ylvisaker D. Conjugate priors for exponential families, Ann. Statist., 7 (2) (1979), pp. 269-281. URL http://dx.doi.org/10.1214/aos/1176344611

Hachemeister, C.A., 1975. Credibility for regression models with application to trend. In: Proc. of the Berkeley Actuarial Research Conference on Credibility, pp. 129–163.

Jewell W.S.Credible means are exact Bayesian for exponential familiesAstin Bull., 8 (1) (1974), pp. 77-90

Johnson N.L. Uniqueness of a result in the theory of accident proneness, Biometrika, 44 (1957), pp. 530-531

Jørgensen B. The Theory of Exponential Dispersion Models and Analysis of Deviance, Instituto de Matemática Pura e Aplicada, (IMPA), Brazil (1992)

Jørgensen B. The Theory of Dispersion Models, Chapman & Hall, London (1997)

Kaas R., Goovaerts M., Dhaene J., Denuit M. Modern Actuarial Risk Theory, Springer-Verlag, Berlin Heidelberg (2008)

Kullback S.Information Theory and Statistics, Dover Publications, New York (1968)

Kullback S., Leibler R.A.On information and sufficiency, Ann. Math. Statist., 22 (1) (1951), pp. 79-86. URL http://dx.doi.org/10.1214/aoms/1177729694

Landsman Z.M., Makov U.E. Exponential dispersion models and credibility, Scand. Actuar. J., 1998 (1) (1998), pp. 89-96. URL http://dx.doi.org/10.1080/03461238.1998.10413995

Nelder J.A., Verall R.J. Credibility theory and generalized linear models. Astin Bull., 27 (1) (1997), pp. 71-82

Nelder J.A., Wedderburn R.W.M.Generalized linear models, J. Roy. Statist. Soc. Ser. A, Gen., 135 (1972), pp. 370-384

Ohlsson E. Combining generalized linear models and credibility models in practice, Scand. Actuar. J., 2008 (4) (2008), pp. 301-314

R Core Team, 2017. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, URL https://www.R-project.org/.

Stan Development Team, 2016. RStan: the R interface to Stan, URL http://mc-stan.org/. R package version 2.14.1.
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