Robust Bayesian bonus-malus premiums under the conditional specification model |
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Authors: | Emilio Gómez Déniz José María Sarabia F. José Vázquez Polo |
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Affiliation: | (1) Department of Quantitative Methods in Economics, University of Las Palmas de Gran Canaria, 35017 Las Palmas de G.C., Spain;(2) Department of Economics, University of Cantabria, 39005 Santander, Spain |
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Abstract: | The conditional specification technique introduced by Arnold et al. (Conditional specification of statistical models. Springer series in statistics. Springer, New York, 1999) was used in Sarabia et al. (Astin Bull 34(1):85–98, 2004) to obtain bonus-malus premiums. The Poisson distribution for which the parameter is a function of the classical structure parameter was used and a new class of prior distributions appeared in a natural way. This model contains, as a particular case, the classical compound Poisson model. In the present paper, the Bayesian robustness of this new model is examined and found to be much more robust than in the classical model in Gómez et al. (Insur Math Econ 31:105–113, 2002). For the present study, the moment conditions on the prior distribution are required. Examples, with real data, are given to illustrate our ideas under the net and exponential premium principles. |
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Keywords: | Conditional specification model Bonus-Malus systems Bayesian robustness |
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