IDEAS home Printed from https://ideas.repec.org/a/bpj/strimo/v31y2014i1p26n3.html

Complete duality for quasiconvex dynamic risk measures on modules of the Lp-type

Author

Listed:
  • Frittelli Marco

    (Dipartimento di Matematica, Università degli Studi di Milano)

  • Maggis Marco

    (Dipartimento di Matematica Università degli Studi di Milano)

Abstract

In the conditional setting we provide a complete duality between quasiconvex risk measures defined on L0 modules of the Lp type and the appropriate class of dual functions. This is based on a general result which extends the usual Penot-Volle representation for quasiconvex real valued maps.

Suggested Citation

  • Frittelli Marco & Maggis Marco, 2014. "Complete duality for quasiconvex dynamic risk measures on modules of the Lp-type," Statistics & Risk Modeling, De Gruyter, vol. 31(1), pages 103-128, March.
    • Handle: RePEc:bpj:strimo:v:31:y:2014:i:1:p:26:n:3
    DOI: 10.1515/strm-2013-1163
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/strm-2013-1163
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/strm-2013-1163?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

    for a different version of it.

    References listed on IDEAS

    as
    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. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    3. Samuel Drapeau & Michael Kupper, 2013. "Risk Preferences and Their Robust Representation," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 28-62, February.
    4. Tiexin Guo, 2010. "Recent progress in random metric theory and its applications to conditional risk measures," Papers 1006.0697, arXiv.org, revised Mar 2011.
    5. repec:hum:wpaper:sfb649dp2005-006 is not listed on IDEAS
    6. Marco Frittelli & Marco Maggis, 2011. "Conditional Certainty Equivalent," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 41-59.
    7. Jean-Paul Penot & Michel Volle, 1990. "On Quasi-Convex Duality," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 597-625, November.
    8. Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
    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. c{C}au{g}{i}n Ararat & Mucahit Aygun, 2021. "Dual representations for quasiconvex compositions with applications to systemic risk measures," Papers 2108.12910, arXiv.org, revised Nov 2025.

    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. Andreas H Hamel, 2018. "Monetary Measures of Risk," Papers 1812.04354, arXiv.org.
    2. Elisa Mastrogiacomo & Emanuela Rosazza Gianin, 2015. "Portfolio Optimization with Quasiconvex Risk Measures," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 1042-1059, October.
    3. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2014. "A unified approach to time consistency of dynamic risk measures and dynamic performance measures in discrete time," Papers 1409.7028, arXiv.org, revised Sep 2017.
    4. Centrone, Francesca & Rosazza Gianin, Emanuela, 2018. "Capital allocation à la Aumann–Shapley for non-differentiable risk measures," European Journal of Operational Research, Elsevier, vol. 267(2), pages 667-675.
    5. Elisa Mastrogiacomo & Emanuela Rosazza Gianin, 2019. "Time-consistency of risk measures: how strong is such a property?," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 287-317, June.
    6. Drapeau, Samuel & Jamneshan, Asgar, 2016. "Conditional preference orders and their numerical representations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 106-118.
    7. Cosimo Munari & Stefan Weber & Lutz Wilhelmy, 2023. "Capital requirements and claims recovery: A new perspective on solvency regulation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(2), pages 329-380, June.
    8. Righi, Marcelo Brutti, 2024. "Star-shaped acceptability indexes," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 170-181.
    9. Alessandro Calvia & Emanuela Rosazza Gianin, 2019. "Risk measures and progressive enlargement of filtration: a BSDE approach," Papers 1904.13257, arXiv.org, revised Mar 2020.
    10. Maria Arduca & Cosimo Munari, 2021. "Risk measures beyond frictionless markets," Papers 2111.08294, arXiv.org.
    11. Samuel Drapeau & Michael Kupper, 2013. "Risk Preferences and Their Robust Representation," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 28-62, February.
    12. c{C}au{g}{i}n Ararat & Bar{i}c{s} Bilir & Elisa Mastrogiacomo, 2022. "Decomposable sums and their implications on naturally quasiconvex risk measures," Papers 2201.05686, arXiv.org.
    13. Zang, Xin & Jiang, Fan & Xia, Chenxi & Yang, Jingping, 2024. "Random distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 51-73.
    14. Marco Frittelli & Marco Maggis, 2017. "Disentangling Price, Risk and Model Risk: V&R measures," Papers 1703.01329, arXiv.org, revised Jul 2017.
    15. Marco Frittelli & Marco Maggis, 2012. "Complete duality for quasiconvex dynamic risk measures on modules of the $L^{p}$-type," Papers 1201.1788, arXiv.org, revised Sep 2012.
    16. Elisa Mastrogiacomo & Emanuela Rosazza Gianin, 2015. "Time-consistency of cash-subadditive risk measures," Papers 1512.03641, arXiv.org.
    17. Alessandro Doldi & Marco Frittelli, 2021. "Real-Valued Systemic Risk Measures," Mathematics, MDPI, vol. 9(9), pages 1-24, April.
    18. Ji, Ronglin & Shi, Xuejun & Wang, Shijie & Zhou, Jinming, 2019. "Dynamic risk measures for processes via backward stochastic differential equations," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 43-50.
    19. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
    20. Tomasz R. Bielecki & Igor Cialenco & Hao Liu, 2023. "Time consistency of dynamic risk measures and dynamic performance measures generated by distortion functions," Papers 2309.02570, arXiv.org, revised Sep 2023.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    Statistics

    Access and download statistics

    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:bpj:strimo:v:31:y:2014:i:1:p:26:n:3. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyterbrill.com .

    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.