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On the independence between risk profiles in the compound collective risk actuarial model. (English) Zbl 1306.91082

Summary: This paper examines a compound collective risk model in which the primary distribution comprised the Poisson-Lindley distribution with a \(\lambda \) parameter, and where the secondary distribution is an exponential one with a \(\theta \) parameter. We consider the case of dependence between risk profiles (i.e., the parameters \(\lambda \) and \(\theta \)), where the dependence is modelled by a Farlie-Gumbel-Morgenstern family. We analyze the consequences of the dependence on the Bayes premium. We conclude that the consequences of the dependence on the Bayes premium may vary considerably.

MSC:

91B30 Risk theory, insurance (MSC2010)
60E05 Probability distributions: general theory
62F15 Bayesian inference
62P05 Applications of statistics to actuarial sciences and financial mathematics

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