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.
翻译:当依赖性结构由Farlie-Gumberl-Morgenster coupula界定时,我们研究基于Copula的集体风险模型。我们利用Farlie-Gumberl-Morgenster coulus和多变量对称Bernoulli分布等级之间的一对一对应法,发现时间的封闭式表达方式,Laplace-Stieltjes从依赖性女性生殖器的集体风险模型中定义的总立体变换方式。此外,即使Farlie-Gumberl-Morgenster coula可能只引起中度依赖性,我们通过数字例子说明,依赖性的累积效应可以为这些集体风险模型中的预期价值、标准偏差、尾巴-Value-at-Risk和总体损失风险的昆虫风险评估生成大量数值。