On the independence between risk profiles in the compound collective risk actuarial model

Abstract

This paper examines a compound collective risk model in which the primary distribution comprised the Poisson-Lindley distribution with a λ parameter, and where the secondary distribution is an exponential one with a θ parameter. We consider the case of dependence between risk profiles (i.e., the parameters λ and θ), 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.