论文标题
与FGM Copulas的风险聚集
Risk aggregation with FGM copulas
论文作者
论文摘要
我们提供了有关女性女外汇Copulas风险汇总的新观点。在此过程中，我们发现了新的结果并重新审视了现有结果，提供了比现有文献中发现的更简单的公式。本文以对称多元伯努利分布和订单统计数据为基础，建立在FGM Copulas的两个新颖表示的基础上。首先，我们详细介绍了具有闭合分布溶液的多元分布的家族，以累积分布函数或骨料随机变量的矩。我们在凸顺序下订购汇总随机变量，并提供在边际离散时计算聚集体RV的累积分布函数的方法。最后，我们讨论了风险分担和资本分配，为每个人提供了数值示例。
We offer a new perspective on risk aggregation with FGM copulas. Along the way, we discover new results and revisit existing ones, providing simpler formulas than one can find in the existing literature. This paper builds on two novel representations of FGM copulas based on symmetric multivariate Bernoulli distributions and order statistics. First, we detail families of multivariate distributions with closed-form solutions for the cumulative distribution function or moments of the aggregate random variables. We order aggregate random variables under the convex order and provide methods to compute the cumulative distribution function of aggregate rvs when the marginals are discrete. Finally, we discuss risk-sharing and capital allocation, providing numerical examples for each.
