[1]温利民,李俊雪,王正武,等.在帕累托模型中风险度量的统计分析[J].江西师范大学学报(自然科学版),2021,(02):211-216.[doi:10.16357/j.cnki.issn1000-5862.2021.02.16]
　WEN Limin,LI Junxue,WANG Zhengwu,et al.The Statistical Analysis of Risk Measure in Pareto Risk Model[J].Journal of Jiangxi Normal University:Natural Science Edition,2021,(02):211-216.[doi:10.16357/j.cnki.issn1000-5862.2021.02.16]
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在帕累托模型中风险度量的统计分析()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2021年02期
页码:
211-216
栏目:
数学与应用数学
出版日期:
2021-04-10

文章信息/Info

Title:
The Statistical Analysis of Risk Measure in Pareto Risk Model
文章编号:
1000-5862(2021)02-0211-06
作者:
温利民; 李俊雪; 王正武; 李 玮
江西师范大学数学与统计学院,江西 南昌 330022
Author(s):
WEN Limin; LI Junxue; WANG Zhengwu; LI Wei
School of Mathematics and Statistics,Jiangxi Normal University,Nanchang Jiangxi 330022,China
关键词:
在险价值;  风险度量;  相合性;  渐近正态性
Keywords:
value at risk;  risk measure;  consistency;  asymptotic normality
分类号:
O 212.1
DOI:
10.16357/j.cnki.issn1000-5862.2021.02.16
文献标志码:
A
摘要:
在帕累托风险模型中,该文研究了在险价值及其相关风险度量的关系,给出了在险价值、期望短缺、尾条件期望、条件在险价值等风险度量的计算方法; 进而,利用极大似然法和矩估计法得到了这些风险度量的估计,证明了估计的相合性和渐近正态性; 最后利用数值模拟的方法验证了在不同样本下估计的收敛速度.
Abstract:
In the Pareto risk model,the relationship between the VaR and its associated risk measure is discussed,and the expressions of value at risk,expectation shortfall,tail value at risk and conditional value at risk are given.Furthermore,the estimation of these risk measures is obtained by using the maximum likelihood method and the moment estimation method,and the consistency and asymptotic normality of those estimators are also proved.Finally,the numerical simulation method is used to verify the convergence rate under different samples.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2020-12-05
基金项目:国家自然科学基金(71761019)和江西省自然科学基金(20203ACB21227)资助项目.
作者简介:温利民(1979—),男,江西石城人,教授,博士,博士生导师,主要从事数理统计与风险管理研究.E-mail:wlmjxnu@163.com
更新日期/Last Update: 2021-04-10