Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (1): 172-183.

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

Guodong Xing1,2,*(),Xiaohu Li3,Suling Kang4,Huangping Shi1   

  1. 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)

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

CLC Number: 

  • O211.9
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