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

On some universal σ-finite measures related to a remarkable class of submartingales

Contents:

Author Info

  • Najnudel, Joseph
  • Nikeghbali, Ashkan
Registered author(s):

    Abstract

    In this paper, for any submartingale of class (Σ) defined on a filtered probability space (Ω,F,P,(Ft)t≥0) satisfying some technical conditions, we associate a σ-finite measure Q on (Ω,F), such that for all t≥0, and for all events Λt∈Ft: Q[Λt,g≤t]=EP[1ΛtXt], where g is the last time for which the process X hits zero. The existence of Q has already been proven in several particular cases, some of them are related with Brownian penalization, and others are involved with problems in mathematical finance. More precisely, the existence of Q in the general case gives an answer to a problem stated by Madan, Roynette and Yor, in a paper about the link between the Black–Scholes formula and the last passage times of some particular submartingales. Moreover, the equality defining Q still holds if the fixed time t is replaced by any bounded stopping time. This generalization can be considered as an extension of Doob’s optional stopping theorem.

    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/pii/S0304414912000191
    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): 122 (2012)
    Issue (Month): 4 ()
    Pages: 1582-1600

    as in new window
    Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1582-1600

    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: Martingale; Submartingale of class (Σ); σ-finite measure; Last hitting time; Doob’s optional stopping theorem;

    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. Laurent Carraro & Nicole El Karoui & Jan Ob{\l}\'oj, 2009. "On Az\'ema-Yor processes, their optimal properties and the Bachelier-drawdown equation," Papers 0902.1328, arXiv.org, revised Sep 2012.
    2. Nikeghbali, Ashkan, 2006. "A class of remarkable submartingales," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 116(6), pages 917-938, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    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:122:y:2012:i:4:p:1582-1600. 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.