一个关于多元正则变化风险的渐近投资组合损失序的注记

数学物理学报 ›› 2019, Vol. 39 ›› Issue (1): 172-183.

一个关于多元正则变化风险的渐近投资组合损失序的注记

邢国东^1,^2,*(),李效虎³,康素玲⁴,石黄萍¹

¹ 上饶师范学院数学与计算机科学学院江西上饶 334001
² 厦门大学数学科学学院福建厦门 361005
³ 史蒂文斯理工学院数学科学系美国新泽西霍博肯 07030
⁴ 合肥学院数学与物理系合肥 230601

收稿日期:2017-06-30 出版日期:2019-02-26 发布日期:2019-03-12
通讯作者: 邢国东 E-mail:xingguodxmu@sina.com
基金资助:
国家自然科学基金(11461009);2018年度安徽高校自然科学研究重点项目(KJ2018A0564);上饶师范学院自科项目(201804);上饶师范学院自科项目(201606)

A Note on Asymptotic Portfolio Loss Order of Multivariate Regularly Varying Risks

Guodong Xing^1,^2,*(),Xiaohu Li³,Suling Kang⁴,Huangping Shi¹

¹ School of Mathematics & Computer Science, Shangrao Normal University, Jiangxi Shangrao 334001
² School of Mathematical Sciences, Xiamen University, Fujian Xiamen 361005
³ Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA
⁴ Department of Mathematics & Physics, Hefei University, Hefei 230601

Received:2017-06-30 Online:2019-02-26 Published:2019-03-12
Contact: Guodong Xing E-mail:xingguodxmu@sina.com
Supported by:
the NSFC(11461009);the Key Projects of Natural Science Research in Universityes of Anhui Province in 2018(KJ2018A0564);the Natural Science Foundation of Shangrao Normal University(201804);the Natural Science Foundation of Shangrao Normal University(201606)

摘要/Abstract

摘要：

在多元正则变化结构下为了渐近量化极值投资组合损失的尾部概率的比值，该文研究了强渐近投资组合序.得到了此序的充分和必要准则.所得到的结果补充并改进了文献[8]所给出的对应的结果.也给出了一个相关的例子作为例证.

关键词: 正则谱测度, 极值风险指数, 多元正则变化, 随机序

Abstract:

This paper studies the stronger asymptotic portfolio loss order to asymptotically quantify the ratio of tail probabilities of extreme portfolio losses in the context of multivariate regular variation. We derive for this order the sufficient and necessary criteria, which supplement and improve the corresponding results due to Mainik and Rüschendorf (2012). Some relevant examples are presented as illustrations as well.

Key words: Canonical spectral measure, Extreme risk index, Multivariate regular variation, Stochastic orders

中图分类号:

O211.9

邢国东,李效虎,康素玲,石黄萍. 一个关于多元正则变化风险的渐近投资组合损失序的注记[J]. 数学物理学报, 2019, 39(1): 172-183.

Guodong Xing,Xiaohu Li,Suling Kang,Huangping Shi. A Note on Asymptotic Portfolio Loss Order of Multivariate Regularly Varying Risks[J]. Acta mathematica scientia,Series A, 2019, 39(1): 172-183.

图/表 3

参考文献 11

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3	de Haan L , Ferreira A . Extreme Value Theory. New York: Springer, 2006
4	Hua L , Joe H . Second order regular variation and conditional tail expectation of multiple risks. Insurance:Mathmatics and Economics, 2011, 49: 537- 546 doi: 10.1016/j.insmatheco.2011.08.013
5	Hult H , Lindskog F . Multivariate extremes, aggregation and dependence in elliptical distributions. Advances in Applied Probability, 2002, 34 (3): 587- 608 doi: 10.1239/aap/1033662167
6	Mainik G. On Asymptotic Diversification Effects for Heavy-Tailed Risks[D]. Freiburg: University of Freiburg, 2010
7	Mainik G , Rüschendorf L . On optimal portfolio diversification with respect to extreme risks. Finance and Stochastics, 2010, 14: 593- 623 doi: 10.1007/s00780-010-0122-z
8	Mainik G , Rüschendorf L . Ordering of multivariate risk models with respect to extreme portfolio losses. Statistics & Risk Modelling, 2012, 29: 73- 105
9	Mainik G , Embrechts P . Diversification in heavy-tailed portfolios:properties and pitfalls. Annals of Actuarial Science, 2013, 7 (1): 26- 45 doi: 10.1017/S1748499512000280
10	Sidney I R . Extreme Values, Regular Variation, and Point Processes. New York: Springer-Verlag, 1987
11	Sidney I R . Heavy-Tail Phenomena. New York: Springer, 2007

${\bf w}$	${\bf w}_1$	${\bf w}_2$	${\bf w}_3$	${\bf w}_4$
$L_{{\bf w}}$	0.8789	0.8514	0.8128	0.7783

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