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Open AccessOpen Access JUSTC Mathematics/Management Article 24 June 2022

Worst-case conditional value-at-risk and conditional expected shortfall based on covariance information

  • Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China

Cite this: JUSTC, 2022, 52(5): 4
https://doi.org/10.52396/JUSTC-2022-0023
CSTR: 32290.14.JUSTC-2022-0023
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  • Author Bio:

    Tiantian Mao is an Associate Professor with the University of Science and Technology of China (USTC). In 2012, she received her Ph.D. degree in Science from USTC. In May of the same year, she joined the Department of Statistics and Finance, School of Management, USTC, for postdoctoral work. Her research fields include risk measurement, risk management, random dominance and extreme value theory

    Qinyu Wu is currently a Ph.D. candidate at the School of Management, University of Science and Technology of China. His research interests focus on risk management and mathematical finance

  • Corresponding author:

    Qinyu Wu, E-mail: wu051555@mail.ustc.edu.cn

  • Received Date: January 24, 2022
  • Accepted Date: March 29, 2022
  • Available Online: June 24, 2022
    Abstract

  • In this paper, we study the worst-case conditional value-at-risk (CoVaR) and conditional expected shortfall (CoES) in a situation where only partial information on the underlying probability distribution is available. In the case of the first two marginal moments are known, the closed-form solution and the value of the worst-case CoVaR and CoES are derived. The worst-case CoVaR and CoES under mean and covariance information are also investigated.

    We construct the above new ambiguity set, then propose the optimization problem of CoVaRand CoES based on this ambiguity set, and give the theoretical results.

    Public Summary

    • The relationship between CoVaR, CoES and dependence structure are investigated.
    • In case where the first two marginal moments are known, the closed-form solution and the valueof the worst-case CoVaR and CoES are derived.
    • The worst-case CoVaR and CoES under mean and covariance information are investigated.
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    Figure  1.   CoVaR and CoES with bivariate Gaussian distributions.

    Figure  2.   CoVaR and CoES with bivariate t-distributions.

    Figure  3.   CoVaR and CoES with Pareto marginal and different copulas.

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