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Non-Cash Risk Measure on Nonconvex Sets

Author

Listed:
  • Chang Cong

    (School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
    These authors contributed equally to this work.)

  • Peibiao Zhao

    (School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
    These authors contributed equally to this work.)

Abstract

Monetary risk measures defined on a convex set are interpreted as the smallest amount of external cash that must be added to a portfolio to make the portfolio being acceptable. In the present paper, the authors introduce a new concept: non-cash risk measure, which does as a nonconvex risk measure work in a nonconvex set. In addition, the authors arrive at a convex extension of the non-cash risk measure, and offer the relationship between the non-cash risk measure and its extension.

Suggested Citation

  • Chang Cong & Peibiao Zhao, 2018. "Non-Cash Risk Measure on Nonconvex Sets," Mathematics, MDPI, vol. 6(10), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:10:p:186-:d:173306
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    References listed on IDEAS

    as
    1. J. Vakili, 2017. "New Models for Computing the Distance of DMUs to the Weak Efficient Boundary of Convex and Nonconvex PPSs in DEA," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-20, December.
    2. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    3. Frey, Rudiger & McNeil, Alexander J., 2002. "VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1317-1334, July.
    4. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    Cited by:

    1. Jun Zhao & Emmanuel Lépinette & Peibiao Zhao, 2019. "Pricing under dynamic risk measures," Post-Print hal-02135232, HAL.

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