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A Bayesian generalized linear model for the Bornhuetter-Ferguson method of claims reserving. (English) Zbl 1085.62516

Summary: This paper shows how Bayesian models within the framework of generalized linear models can be applied to claims reserving. The author demonstrates that this approach is closely related to the Bornhuetter-Ferguson technique. Benktander (1976) and Mack (2000) previously studied the Bornhuetter-Ferguson technique and advocated using credibility models. The present paper uses a Bayesian parametric model within the framework of generalized linear models.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62F15 Bayesian inference
62J12 Generalized linear models (logistic models)

Software:

BUGS
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References:

[1] Benktander Gunnar, The Actuarial Review (1976)
[2] Bornhuetter Ronald L., Proceedings of the Casualty Actuarial Society 59 pp 181– (1972)
[3] De Alba Enrique, North American Actuarial Journal 6 (4) pp 1– (2002)
[4] England Peter D., British Actuarial Journal pp 443– (2002)
[5] Ntzoufras Ioannis, North American Actuarial Journal 6 (1) pp 113– (2002)
[6] Mack Thomas, ASTIN Bulletin 30 pp 333– (2000) · Zbl 1087.91514
[7] Renshaw Arthur E., British Actuarial Journal 4 (4) pp 903– (1998)
[8] Scollnik David P. M., North American Actuarial Journal 5 (2) pp 96– (2001)
[9] Spiegelhalter David J., BUGS 0.5: Bayesian inference using gibbs sampling (1996)
[10] Taylor Greg C., Loss Reserving: An Actuarial Perspective (2000)
[11] Verrall Richard J., Insurance: Mathematics & Economics 26 pp 91– (2000) · Zbl 1072.62654
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