Asymptotic Behaviors of the VaR and CVaR Estimates for Widely Orthant Dependent Sequences

IF 1 4区数学 Q3 STATISTICS & PROBABILITY

Methodology and Computing in Applied Probability Pub Date : 2024-07-06 DOI:10.1007/s11009-024-10093-y

Li Yongming, Li Naiyi, Luo Zhongde, Xing Guodong

引用次数: 0

Abstract

This paper considers some asymptotics of value-at-risk (VaR) and conditional value-at-risk (CVaR) estimates in the cases of extended negatively dependent (END) and widely orthant dependent (WOD) sequences. The Bahadur representation and strong consistency of VaR estimator are obtained, and the strong convergence rate of CVaR estimator is obtained based on END and WOD sequences. In addition, the asymptotic normality of VaR estimator is given based on END sequence. Finally, some simulations to study the numerical performance of the consistency for VaR and CVaR estimators are given in the case of WOD sample. Our results extend and improve some corresponding results.

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宽正交依赖序列的 VaR 和 CVaR 估计值的渐近行为

本文考虑了在扩展负相关（END）和广泛正相关（WOD）序列情况下风险价值（VaR）和条件风险价值（CVaR）估计的一些渐近性。基于END和WOD序列，得到了VaR估计器的Bahadur表示和强一致性，并得到了CVaR估计器的强收敛率。此外，基于END序列给出了VaR估计器的渐近正态性。最后，在 WOD 样本的情况下，给出了一些模拟来研究 VaR 和 CVaR 估计器一致性的数值表现。我们的结果扩展并改进了一些相应的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Methodology and Computing in Applied Probability 数学-统计学与概率论

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Methodology and Computing in Applied Probability will publish high quality research and review articles in the areas of applied probability that emphasize methodology and computing. Of special interest are articles in important areas of applications that include detailed case studies. Applied probability is a broad research area that is of interest to many scientists in diverse disciplines including: anthropology, biology, communication theory, economics, epidemiology, finance, linguistics, meteorology, operations research, psychology, quality control, reliability theory, sociology and statistics. The following alphabetical listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interests: -Algorithms- Approximations- Asymptotic Approximations & Expansions- Combinatorial & Geometric Probability- Communication Networks- Extreme Value Theory- Finance- Image Analysis- Inequalities- Information Theory- Mathematical Physics- Molecular Biology- Monte Carlo Methods- Order Statistics- Queuing Theory- Reliability Theory- Stochastic Processes