IDEAS home Printed from https://ideas.repec.org/p/cfi/fseres/cf287.html
   My bibliography  Save this paper

Maximum Lebesgue Extension Of Convex Risk Measures

Author

Listed:
  • Keita Owari

    (Graduate School of Economics, University of Tokyo, Tokyo)

Abstract

Given a convex risk measure on $L^\infty$ having the Lebesgue property, we construct a solid space of random variables on which the original risk measure is extended preserving the Lebesgue property (on the entire space). This space is an order-continuous Banach lattice, and is maximum among all solid spaces admitting such a regular extension. We then characterize the space in terms of uniform integrability of certain families. As a byproduct, we present a generalization of Jouini-Schachermayer-Touzi’s theorem on the weakcompactness characterization of Lebesgue property, which is valid for any solid vector spaces of random variables, and does not require any topological property of the space.

Suggested Citation

  • Keita Owari, 2012. "Maximum Lebesgue Extension Of Convex Risk Measures," CARF F-Series CARF-F-287, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf287
    as

    Download full text from publisher

    File URL: https://www.carf.e.u-tokyo.ac.jp/old/pdf/workingpaper/fseries/299.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Freddy Delbaen, 2009. "Risk Measures For Non‐Integrable Random Variables," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 329-333, April.
    2. Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2005. "Coherent and convex monetary risk measures for unbounded càdlàg processes," Finance and Stochastics, Springer, vol. 9(3), pages 369-387, July.
    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. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
    5. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
    Full references (including those not matched with items on IDEAS)

    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. Keita Owari, 2013. "Maximum Lebesgue Extension of Monotone Convex Functions," CARF F-Series CARF-F-315, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Marcelo Brutti Righi, 2017. "Closed spaces induced by deviation measures," Economics Bulletin, AccessEcon, vol. 37(3), pages 1781-1784.
    3. Kovacevic Raimund M., 2012. "Conditional risk and acceptability mappings as Banach-lattice valued mappings," Statistics & Risk Modeling, De Gruyter, vol. 29(1), pages 1-18, March.
    4. Niushan Gao & Foivos Xanthos, 2015. "On the C-property and $w^*$-representations of risk measures," Papers 1511.03159, arXiv.org, revised Sep 2016.
    5. Samuel Drapeau & Michael Kupper, 2013. "Risk Preferences and Their Robust Representation," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 28-62, February.
    6. Kountzakis, C. & Polyrakis, I.A., 2013. "Coherent risk measures in general economic models and price bubbles," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 201-209.
    7. Niushan Gao & Denny H. Leung & Cosimo Munari & Foivos Xanthos, 2017. "Fatou Property, representations, and extensions of law-invariant risk measures on general Orlicz spaces," Papers 1701.05967, arXiv.org, revised Sep 2017.
    8. Farkas, Walter & Koch-Medina, Pablo & Munari, Cosimo, 2014. "Capital requirements with defaultable securities," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 58-67.
    9. Pichler, Alois, 2013. "The natural Banach space for version independent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 405-415.
    10. Svindland Gregor, 2009. "Subgradients of law-invariant convex risk measures on L," Statistics & Risk Modeling, De Gruyter, vol. 27(2), pages 169-199, December.
    11. Felix-Benedikt Liebrich & Gregor Svindland, 2018. "Risk sharing for capital requirements with multidimensional security markets," Papers 1809.10015, arXiv.org.
    12. Andreas H Hamel, 2018. "Monetary Measures of Risk," Papers 1812.04354, arXiv.org.
    13. Martin Herdegen & Nazem Khan, 2022. "$\rho$-arbitrage and $\rho$-consistent pricing for star-shaped risk measures," Papers 2202.07610, arXiv.org, revised Feb 2024.
    14. Niushan Gao & Denny H. Leung & Foivos Xanthos, 2016. "Closedness of convex sets in Orlicz spaces with applications to dual representation of risk measures," Papers 1610.08806, arXiv.org, revised Jun 2017.
    15. Daniel Bartl, 2016. "Conditional nonlinear expectations," Papers 1612.09103, arXiv.org, revised Mar 2019.
    16. 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.
    17. Niushan Gao & Denny Leung & Cosimo Munari & Foivos Xanthos, 2018. "Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces," Finance and Stochastics, Springer, vol. 22(2), pages 395-415, April.
    18. Christos E. Kountzakis & Damiano Rossello, 2022. "Monetary risk measures for stochastic processes via Orlicz duality," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 35-56, June.
    19. Sascha Desmettre & Christian Laudagé & Jörn Sass, 2020. "Good-Deal Bounds for Option Prices under Value-at-Risk and Expected Shortfall Constraints," Risks, MDPI, vol. 8(4), pages 1-22, October.
    20. Fabio Bellini & Pablo Koch-Medina & Cosimo Munari & Gregor Svindland, 2018. "Law-invariant functionals on general spaces of random variables," Papers 1808.00821, arXiv.org, revised Jan 2021.

    More about this item

    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:cfi:fseres:cf287. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/catokjp.html .

    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.