一种多元Pareto分布及其在金融风险度量中的应用
A form of multivariate Pareto distribution with applications to financial risk measurement
摘要：
引入了一种新的具有任意参数化和正相依的单变量Pareto边缘的多元分布。与Asimit等人（2010）的概率定律不同[Asimit，V.，Furman，E.和Vernic，R.（2010）关于多变量帕累托分布。保险费：Mathematics and Economics 46（2），308-316]，本文的结构相对于相应的勒贝格测度是绝对连续的。该分布对精算师来说很重要，因为它与流行的脆弱性模型有联系，也因为它能够描述相关的重尾风险。新的分布的成因与一些现有的概率模型，并证明了有用的特征结果。例如，建立了累积分布和概率密度函数、联合矩和回归方程。利用最小值和最大值的分布以及一些加权风险度量，讨论了该分布在保险中的应用。
英文摘要：
A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a multivariate Pareto distribution. Insurance: Mathematics and Economics 46(2), 308-316], the structure in this paper is absolutely continuous with respect to the corresponding Lebesgue measure. The distribution is of importance to actuaries through its connections to the popular frailty models, as well as because of the capacity to describe dependent heavy-tailed risks. The genesis of the new distribution is linked to a number of existing probability models, and useful characteristic results are proved. Expressions for, e.g., the decumulative distribution and probability density functions, (joint) moments and regressions are developed. The distributions of minima and maxima, as well as, some weighted risk measures are employed to exemplify possible applications of the distribution in insurance.
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