Bounds for sums of non-independent log-elliptical random variables
为非独立对数椭圆随机变量之和的分布构造了上下界，扩展了对数正态随机变量之和的界的结果，对金融和保险中的风险聚合有参考价值。
In this paper, we construct upper and lower bounds for the distribution of a sum of non-independent log-elliptical random variables. These bounds are applications of the ideas developed in Kaas, Dhaene & Goovaerts (2000). The class of multivariate log-elliptical random variables is an extension of the class of multivariate log-normal random variables. Hence, the results presented here are natural extensions of the results presented in Dhaene, Denuit, Goovaerts, Kaas & Vyncke (2002a, 2002b), where bounds for sums of log-normal random variables were derived. The upper bound is based on the idea of replacing the sum of log-elliptical random variables by a sum of random variables with the same marginals, but with a dependency structure described by the comonotonic copula. Lower bounds and improved upper bounds are constructed by including additional information about the dependency structure by introducing some conditioning random variable.