IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v184y2022ics016771522100290x.html
   My bibliography  Save this article

On the link between monetary and star-shaped risk measures

Author

Listed:
  • Moresco, Marlon Ruoso
  • Righi, Marcelo Brutti

Abstract

Recently, Castagnoli et al. (2021) introduced the class of star-shaped risk measures as a generalization of convex and coherent ones, proving that there is a representation as the pointwise minimum of some family composed by convex risk measures. Concomitantly, Jia et al. (2020) prove a similar representation result for monetary risk measures, which are more general than star-shaped ones. Then, there is a question on how both classes are connected. In this letter, we provide an answer by casting light on the importance of the acceptability of 0, which is linked to the property of normalization. We then show that under mild conditions, a monetary risk measure is only a translation away from star-shapedness.

Suggested Citation

  • Moresco, Marlon Ruoso & Righi, Marcelo Brutti, 2022. "On the link between monetary and star-shaped risk measures," Statistics & Probability Letters, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:stapro:v:184:y:2022:i:c:s016771522100290x
    DOI: 10.1016/j.spl.2021.109345
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771522100290X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2021.109345?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Guangyan Jia & Jianming Xia & Rongjie Zhao, 2020. "Monetary Risk Measures," Papers 2012.06751, arXiv.org.
    2. Felix-Benedikt Liebrich, 2021. "Risk sharing under heterogeneous beliefs without convexity," Papers 2108.05791, arXiv.org, revised May 2022.
    3. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    4. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    5. Song, Yongsheng & Yan, Jia-An, 2009. "Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 459-465, December.
    6. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    7. Erio Castagnoli & Giacomo Cattelan & Fabio Maccheroni & Claudio Tebaldi & Ruodu Wang, 2021. "Star-shaped Risk Measures," Papers 2103.15790, arXiv.org, revised Apr 2022.
    8. 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.
    9. repec:dau:papers:123456789/342 is not listed on IDEAS
    10. Marcelo Brutti Righi, 2021. "Star-shaped acceptability indexes," Papers 2110.08630, arXiv.org, revised Jun 2022.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Samuel Solgon Santos & Marlon Ruoso Moresco & Marcelo Brutti Righi & Eduardo de Oliveira Horta, 2023. "A note on the induction of comonotonic additive risk measures from acceptance sets," Papers 2307.04647, arXiv.org, revised Jul 2023.
    2. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2022. "Star-Shaped deviations," Papers 2207.08613, arXiv.org.
    3. Marcelo Brutti Righi & Fernanda Maria Muller & Marlon Ruoso Moresco, 2022. "A risk measurement approach from risk-averse stochastic optimization of score functions," Papers 2208.14809, arXiv.org, revised May 2023.
    4. Dejian Tian & Xunlian Wang, 2023. "Dynamic star-shaped risk measures and $g$-expectations," Papers 2305.02481, arXiv.org.
    5. Roger J. A. Laeven & Emanuela Rosazza Gianin & Marco Zullino, 2023. "Dynamic Return and Star-Shaped Risk Measures via BSDEs," Papers 2307.03447, arXiv.org, revised Jul 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marlon Moresco & Marcelo Brutti Righi, 2021. "On the link between monetary and star-shaped risk measures," Papers 2108.13500, arXiv.org.
    2. Xia Han & Qiuqi Wang & Ruodu Wang & Jianming Xia, 2021. "Cash-subadditive risk measures without quasi-convexity," Papers 2110.12198, arXiv.org, revised Mar 2022.
    3. Dejian Tian & Xunlian Wang, 2023. "Dynamic star-shaped risk measures and $g$-expectations," Papers 2305.02481, arXiv.org.
    4. Guangyan Jia & Jianming Xia & Rongjie Zhao, 2020. "Monetary Risk Measures," Papers 2012.06751, arXiv.org.
    5. Yanhong Chen & Yijun Hu, 2019. "Set-Valued Law Invariant Coherent And Convex Risk Measures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-18, May.
    6. Wentao Hu & Cuixia Chen & Yufeng Shi & Ze Chen, 2022. "A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 831-874, June.
    7. Jaume Belles‐Sampera & Montserrat Guillén & Miguel Santolino, 2014. "Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures," Risk Analysis, John Wiley & Sons, vol. 34(1), pages 121-134, January.
    8. Geissel Sebastian & Sass Jörn & Seifried Frank Thomas, 2018. "Optimal expected utility risk measures," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 73-87, January.
    9. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    10. Daniel Lacker, 2018. "Liquidity, Risk Measures, and Concentration of Measure," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 813-837, August.
    11. Gilles Boevi Koumou & Georges Dionne, 2022. "Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation," Risks, MDPI, vol. 10(11), pages 1-19, October.
    12. Maria Arduca & Cosimo Munari, 2021. "Risk measures beyond frictionless markets," Papers 2111.08294, arXiv.org.
    13. Jana Bielagk & Arnaud Lionnet & Gonçalo dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Working Papers hal-01245812, HAL.
    14. Steven Kou & Xianhua Peng & Chris C. Heyde, 2013. "External Risk Measures and Basel Accords," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 393-417, August.
    15. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2020. "Inf-convolution and optimal risk sharing with countable sets of risk measures," Papers 2003.05797, arXiv.org, revised Mar 2022.
    16. Gilles Angelsberg & Freddy Delbaen & Ivo Kaelin & Michael Kupper & Joachim Näf, 2011. "On a class of law invariant convex risk measures," Finance and Stochastics, Springer, vol. 15(2), pages 343-363, June.
    17. Rama Cont & Romain Deguest & Xuedong He, 2011. "Loss-Based Risk Measures," Working Papers hal-00629929, HAL.
    18. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2022. "Star-Shaped deviations," Papers 2207.08613, arXiv.org.
    19. Zou, Zhenfeng & Wu, Qinyu & Xia, Zichao & Hu, Taizhong, 2023. "Adjusted Rényi entropic Value-at-Risk," European Journal of Operational Research, Elsevier, vol. 306(1), pages 255-268.
    20. Andreas H Hamel, 2018. "Monetary Measures of Risk," Papers 1812.04354, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:184:y:2022:i:c:s016771522100290x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.