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Set-Valued Dynamic Risk Measures For Bounded Discrete-Time Processes

Author

Listed:
  • YANHONG CHEN

    (College of Finance and Statistics, Hunan University, Changsha 410082, P. R. China)

  • YIJUN HU

    (School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China)

Abstract

In this paper, we study how to evaluate the risk of a financial portfolio, whose components may be dependent and come from different markets or involve more than one kind of currencies, while we also take into consideration the uncertainty about the time value of money. Namely, we introduce a new class of risk measures, named set-valued dynamic risk measures for bounded discrete-time processes that are adapted to a given filtration. The time horizon can be finite or infinite. We investigate the representation results for them by making full use of Legendre–Fenchel conjugation theory for set-valued functions. Finally, some examples such as the set-valued dynamic average value at risk and the entropic risk measure for bounded discrete-time processes are also given.

Suggested Citation

  • Yanhong Chen & Yijun Hu, 2020. "Set-Valued Dynamic Risk Measures For Bounded Discrete-Time Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(03), pages 1-42, May.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:03:n:s021902492050017x
    DOI: 10.1142/S021902492050017X
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    Citations

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    Cited by:

    1. Yanhong Chen & Zachary Feinstein, 2022. "Set-valued dynamic risk measures for processes and for vectors," Finance and Stochastics, Springer, vol. 26(3), pages 505-533, July.
    2. Yanhong Chen & Zachary Feinstein, 2021. "Set-Valued Dynamic Risk Measures for Processes and Vectors," Papers 2103.00905, arXiv.org, revised Nov 2021.
    3. Bingchu Nie & Dejian Tian & Long Jiang, 2024. "Set-valued Star-Shaped Risk Measures," Papers 2402.18014, arXiv.org.

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