Advanced Search
MyIDEAS: Login to save this article or follow this journal

Time consistent dynamic risk processes

Contents:

Author Info

  • Bion-Nadal, Jocelyne
Registered author(s):

    Abstract

    A crucial property for dynamic risk measures is the time consistency. In this paper, a characterization of time consistency in terms of a "cocycle condition" for the minimal penalty function is proved for general dynamic risk measures continuous from above. Then the question of the regularity of paths is addressed. It is shown that, for a time consistent dynamic risk measure normalized and non-degenerate, the process associated with any bounded random variable has a càdlàg modification, under a mild condition always satisfied in the case of continuity from below. When normalization is not assumed, a right continuity condition on the penalty has to be added. Applying these results and using right continuous BMO martingales, families of not necessarily normalized dynamic risk measures leading to càdlàg paths, and allowing for jumps, are exhibited.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/B6V1B-4S0YXT6-3/2/a22f10ae9c710b85b632179a3e2cd0b6
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 119 (2009)
    Issue (Month): 2 (February)
    Pages: 633-654

    as in new window
    Handle: RePEc:eee:spapps:v:119:y:2009:i:2:p:633-654

    Contact details of provider:
    Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description

    Order Information:
    Postal: http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
    Web: https://shop.elsevier.com/OOC/InitController?id=505572&ref=505572_01_ooc_1&version=01

    Related research

    Keywords: Dynamic risk measures Time consistency BMO martingales Snell envelope;

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    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. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 112(2), pages 185-200, August.
    3. Roorda, Berend & Schumacher, J.M., 2007. "Time consistency conditions for acceptability measures, with an application to Tail Value at Risk," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 209-230, March.
    4. Föllmer Hans & Penner Irina, 2006. "Convex risk measures and the dynamics of their penalty functions," Statistics & Risk Modeling, De Gruyter, De Gruyter, vol. 24(1/2006), pages 36, July.
    5. Jocelyne Bion-Nadal, 2008. "Dynamic risk measures: Time consistency and risk measures from BMO martingales," Finance and Stochastics, Springer, vol. 12(2), pages 219-244, April.
    6. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
    8. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    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 in new window

    Cited by:
    1. Sigrid K\"allblad, 2013. "Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals," Papers 1311.7419, arXiv.org.
    2. Cohen, Samuel N., 2012. "Representing filtration consistent nonlinear expectations as g-expectations in general probability spaces," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 122(4), pages 1601-1626.
    3. Stadje, M.A. & Pelsser, A., 2014. "Time-Consistent and Market-Consistent Evaluations (Revised version of 2012-086)," Discussion Paper, Tilburg University, Center for Economic Research 2014-002, Tilburg University, Center for Economic Research.
    4. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.
    5. Sigrid Kallblad & Jan Obloj & Thaleia Zariphopoulou, 2013. "Time--consistent investment under model uncertainty: the robust forward criteria," Papers 1311.3529, arXiv.org.
    6. Freddy Delbaen & Shige Peng & Emanuela Rosazza Gianin, 2010. "Representation of the penalty term of dynamic concave utilities," Finance and Stochastics, Springer, vol. 14(3), pages 449-472, September.
    7. Matmoura, Yassine & Penev, Spiridon, 2013. "Multistage optimization of option portfolio using higher order coherent risk measures," European Journal of Operational Research, Elsevier, vol. 227(1), pages 190-198.
    8. Pelsser, A. & Stadje, M.A., 2012. "Time-Consistent and Market-Consistent Evaluations (Revised version of CentER DP 2011-063)," Discussion Paper, Tilburg University, Center for Economic Research 2012-086, Tilburg University, Center for Economic Research.
    9. Jocelyne Bion-Nadal & Giulia Nunno, 2013. "Dynamic no-good-deal pricing measures and extension theorems for linear operators on L ∞," Finance and Stochastics, Springer, vol. 17(3), pages 587-613, July.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:119:y:2009:i:2:p:633-654. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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