© Agata Boratyńska. Article available under the CC BY-SA 4.0 licence
ARTICLE
ABSTRACT
This study deals with the problem of robustness of the collective and Bayes premiums under uncertainty of prior knowledge. The inaccuracy of the prior knowledge concerns the disturbance of independence between variables describing the frequency and average value of claims. Traditionally, these variables are independent, but in applications it is not always the case. Two classes of priors are presented: in the first class, the FGM copula is applied, while in the second one, the dependence between two contaminated priors is shown. In both classes, priors have the form of a linear combination of known bivariate probability distributions. The ranges of collective and Bayes premiums are calculated and prior and posterior regret gamma-minimax premiums are presented as the optimal premiums. Despite the very mild or small dependence, its influence on the premiums, especially on the bonus-malus factor, is relatively significant.
KEYWORDS
classes of priors, FGM copula, epsilon-contamination, posterior regret Gamma-minimax premium, mean square error, bonus-malus factor.
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