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Monotone Mean L p -Deviation Risk Measures

Author

Listed:
  • Jinyang Zhang

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

  • Linxiao Wei

    (College of Science, Wuhan University of Technology, Wuhan 430070, China)

  • Yijun Hu

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

Abstract

In this paper, we establish a new coherent risk measure on L p , which we refer to as the monotone mean L p -deviation risk measure. Then, the related properties are discussed. Furthermore, from the perspective of acceptance set, we discuss the relationship between the monotone mean L p -deviation risk measure and the monotone Sharpe ratio risk measure. Finally, we extend the monotone mean L p -deviation risk measure to the multivariate setting.

Suggested Citation

  • Jinyang Zhang & Linxiao Wei & Yijun Hu, 2023. "Monotone Mean L p -Deviation Risk Measures," Mathematics, MDPI, vol. 11(12), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2706-:d:1171345
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    References listed on IDEAS

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    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Burgert, Christian & Ruschendorf, Ludger, 2006. "Consistent risk measures for portfolio vectors," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 289-297, April.
    3. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    4. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, Michael, 2006. "Master funds in portfolio analysis with general deviation measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 743-778, February.
    5. 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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