论文标题
具有FGM依赖的集体风险模型
Collective risk models with FGM dependence
论文作者
论文摘要
当依赖性结构由Farlie-Gumbel-Morgenstern（FGM）Copula定义时，我们研究了基于Copula的集体风险模型。通过利用FGM Copulas类和多元对称的Bernoulli分布之间的一对一对应关系，我们找到了矩和Laplace-Stieltjes转换的方便表示形式，用于由具有FGM依赖性的集体风险模型定义的聚合随机变量。我们研究了该集体风险模型的不同组成部分，旨在更好地了解索赔频率和严重性之间假定依赖性的影响。依靠随机排序，我们分析了依赖性对总索赔量随机变量的影响。即使FGM Copula只能引起中等依赖性，我们通过数值示例说明，FGM依赖性的累积效应可能会导致关键风险度量对集体风险模型定义的聚合随机变量的实质性变化。
We study copula-based collective risk models when the dependence structure is defined by a Farlie-Gumbel-Morgenstern (FGM) copula. By leveraging a one-to-one correspondence between the class of FGM copulas and multivariate symmetric Bernoulli distributions, we find convenient representations for the moments and Laplace-Stieltjes transform for the aggregate random variable defined from collective risk models with FGM dependence. We examine different components of this collective risk model, aiming to better understand the impact of the assumed dependence between a claim's frequency and severity. Relying on stochastic ordering, we analyze the impact of dependence on the aggregate claim amount random variable. Even if the FGM copula may only induce moderate dependence, we illustrate through numerical examples that the cumulative effect of FGM dependence can lead to substantial variations in key risk measures on aggregate random variables defined from collective risk models.
