Collective risk models with FGM dependence
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We study copula-based collective risk models when the dependence structure is defined by a Farlie-Gumbel-Morgenstern copula. By leveraging a one-to-one correspondence between the class of Farlie-Gumbel-Morgenstern copulas and multivariate symmetric Bernoulli distributions, we find closed-form expressions for the moments and Laplace-Stieltjes transform for the aggregate rv defined from collective risk models with FGM dependence. Furthermore, even if the Farlie-Gumbel-Morgenstern copula may only induce moderate dependence, we illustrate through numerical examples that the cumulative effect of dependence can generate large ranges of values for the expected value, the standard deviation, the Tail-Value-at-Risk and the entropic risk measure of aggregate loss rvs within these collective risk models.
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