具有不同椭圆分量的依赖风险随机向量建模

IF 1.5 Q3 BUSINESS, FINANCE
Z. Landsman, T. Shushi
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引用次数: 1

摘要

摘要在金融和精算学中,多变量椭圆分布族是一个著名且广泛使用的连续风险模型。然而,它有一个本质的缺点:它的所有单变量边际分布都是相同的,直到位置和规模变换。例如,多元Student t-分布(椭圆族的一个重要成员)的所有边值都具有相同的自由度。我们引入了一种新的方法来生成一个多变量分布,其边际是椭圆随机变量,而通常情况下,每个风险都有不同的椭圆分布,这在处理保险和金融数据时很重要。该方案是椭圆copula分布的替代方案,在许多情况下,椭圆copula分配很难计算其风险度量和风险资本分配。我们研究了所提出的模型的主要特征:特征和密度函数、期望、协方差矩阵和线性回归向量的期望。我们计算了引入分布的重要风险度量,如风险价值和风险尾值,以及总风险的风险资本分配。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Modelling random vectors of dependent risks with different elliptical components
Abstract In Finance and Actuarial Science, the multivariate elliptical family of distributions is a famous and well-used model for continuous risks. However, it has an essential shortcoming: all its univariate marginal distributions are the same, up to location and scale transformations. For example, all marginals of the multivariate Student’s t-distribution, an important member of the elliptical family, have the same number of degrees of freedom. We introduce a new approach to generate a multivariate distribution whose marginals are elliptical random variables, while in general, each of the risks has different elliptical distribution, which is important when dealing with insurance and financial data. The proposal is an alternative to the elliptical copula distribution where, in many cases, it is very difficult to calculate its risk measures and risk capital allocation. We study the main characteristics of the proposed model: characteristic and density functions, expectations, covariance matrices and expectation of the linear regression vector. We calculate important risk measures for the introduced distributions, such as the value at risk and tail value at risk, and the risk capital allocation of the aggregated risks.
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来源期刊
CiteScore
3.10
自引率
5.90%
发文量
22
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