Extreme negative dependence and risk aggregation

JOURNAL OF MULTIVARIATE ANALYSIS

卷:136

Article

Wang, Bin¹  Wang, Ruodu² 

[1] Beijing Technol & Business Univ, Dept Math, Beijing 100048, Peoples R China

[2] Univ Waterloo, Dept Stat & Actuarial Sci, Waterloo, ON N2L 3G1, Canada

关键词: Negative dependence;    Variance reduction;    Sums of random variables;    Central limit theorem;    Risk aggregation;   

DOI  :  10.1016/j.jmva.2015.01.006

来源: Elsevier

【 摘 要 】

We introduce the concept of an extremely negatively dependent (END) sequence of random variables with a given common marginal distribution. An END sequence has a partial sum which, subtracted by its mean, does not diverge as the number of random variables goes to infinity. We show that an END sequence always exists for any given marginal distributions with a finite mean and we provide a probabilistic construction. Through such a construction, the partial sum of identically distributed but dependent random variables is controlled by a random variable that depends only on the marginal distribution of the sequence. We provide some properties and examples of our construction. The new concept and derived results are used to obtain asymptotic bounds for risk aggregation with dependence uncertainty. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free