On Bounds of Value-at-Risk and Convex Risk Measure of Portfolio of Weighted Dependent Risks

XING Guo-dong, LI Xiao-hu

doi:10.13371/j.cnki.chin.q.j.m.2018.04.009

Chinese Quarterly Journal of Mathematics >

2018 , Vol. 33 >Issue 4: 421 - 433

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2018.04.009

On Bounds of Value-at-Risk and Convex Risk Measure of Portfolio of Weighted Dependent Risks

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School of Mathematics & Computer Science Shangrao Normal University,School of Mathematical Sciences Xiamen University . Department of Mathematical Sciences Stevens Institute of Technology.

XING Guo-dong(1973-), male, native of Wuhu, Anhui, teaching assistant of Shangrao Normal University, eangages in quantitative risk management and statistics.

Accepted date: 2017-04-18

Online published: 2020-10-07

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Abstract

This note analytically derives lower and upper bounds for Value-at-Risk and convex risk measures of a portfolio of weighted risks in the context of positive dependence.The bounds serve as extensions of the corresponding ones due to Bignozzi et al.(2015).Also, DUspread of value-at-risk and expected shortfall of Bignozzi et al.(2015) are also improved in some particular cases.

Key words： DU-spread; Expected shortfall; Lower orthant order; Upper orthant order; Weakly conditional increasing in sequence order

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XING Guo-dong, LI Xiao-hu . On Bounds of Value-at-Risk and Convex Risk Measure of Portfolio of Weighted Dependent Risks[J]. Chinese Quarterly Journal of Mathematics, 2018 , 33(4) : 421 -433 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.04.009

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