论文标题
多元基质 - 指示仿射混合物及其在风险理论中的应用
Multivariate matrix-exponential affine mixtures and their applications in risk theory
论文作者
论文摘要
在本文中，提出了与基质 - 指数边缘的一类多元基质 - 指数仿射混合物。该类显示具有各种有吸引力的特性，例如在尺寸偏见的Esscher变换，顺序统计，剩余寿命和高阶平衡分布下闭合。这允许明确计算各种精算量的兴趣。结果将应用于多种精算问题，包括多元风险措施，总损失，大量索赔再保险，加权保费计算和风险资本分配。此外，考虑了具有依赖风险的乘法背景风险模型，还提供了其资本分配规则。我们通过基于完整数据和潜在研究途径讨论校准方案来最终确定。
In this paper, a class of multivariate matrix-exponential affine mixtures with matrix-exponential marginals is proposed. The class is shown to possess various attractive properties such as closure under size-biased Esscher transform, order statistics, residual lifetime and higher order equilibrium distributions. This allows for explicit calculations of various actuarial quantities of interest. The results are applied in a wide range of actuarial problems including multivariate risk measures, aggregate loss, large claims reinsurance, weighted premium calculations and risk capital allocation. Furthermore, a multiplicative background risk model with dependent risks is considered and its capital allocation rules are provided as well. We finalize by discussing a calibration scheme based on complete data and potential avenues of research.
