多元矩阵-指数仿射混合模型及其在风险理论中的应用
Multivariate matrix-exponential affine mixtures and their applications in risk theory
摘要：
本文提出了一类具有矩阵指数边缘的多元矩阵指数仿射混合。该类具有各种有吸引力的性质，如大小偏置Esscher变换下的封闭性，顺序统计量，剩余寿命和高阶平衡分布。这允许明确计算各种精算量的利益。结果被应用于广泛的精算问题，包括多变量风险度量，总损失，大额索赔再保险，加权保费计算和风险资本分配。在此基础上，考虑了一类具有相关风险的乘性背景风险模型，并给出了其资本分配规则。最后，我们讨论了校准方案的基础上完整的数据和潜在的研究途径。
英文摘要：
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.
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