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

The Compatible Bond-Stock Market With Jumps

Contents:

Author Info

  • DEWEN XIONG

    ()
    (Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, P. R. China)

  • MICHAEL KOHLMANN

    ()
    (Department of Mathematics and Statistics, University of Konstanz, D-78457, Konstanz, Germany)

Registered author(s):

    Abstract

    We construct a bond-stock market composed of d stocks and many bonds with jumps driven by general marked point process as well as by an ℝn-valued Wiener process. By composing these tools we introduce the concept of a compatible bond-stock market and give a necessary and sufficient condition for this property. We study no-arbitrage properties of the composed market where a compatible bond-stock market is arbitrage-free both for the bonds market and for the stocks market.We then turn to an incomplete compatible bond-stock market and give a necessary and sufficient condition for a compatible bond-stock market to be incomplete. In this market we consider the mean-variance hedging in the special situation where both B(u, T) and eG(u, y, T)-1 are quadratic functions of T - u. So, we need to extend the notion of a variance-optimal martingale (VOM) as in Xiong and Kohlmann (2009) to the more general market. By introducing two virtual stocks $\widetilde{S}_1, \widetilde{S}_2$, we prove that the VOM for the bond-stock market is the same as the VOM for the new stock market $\bar{S}, \widetilde{S}_1, \widetilde{S}_2$. The mean-variance hedging problem in this incomplete bond-stock market for a contingent claim $H \in L^2(\mathscr{F}_{T^*})$ is solved by deriving an explicit solution of the optimal measure-valued strategy and the optimal cost induced by the optimal strategy of MHV for the stocks $\bar{S}, \widetilde{S}_1, \widetilde{S}_2$ is computed.

    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.worldscinet.com/cgi-bin/details.cgi?type=pdf&id=pii:S0219024911006449
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: http://www.worldscinet.com/cgi-bin/details.cgi?type=html&id=pii:S0219024911006449
    Download Restriction: Access to full text is restricted to subscribers.

    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 World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 14 (2011)
    Issue (Month): 05 ()
    Pages: 723-755

    as in new window
    Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:05:p:723-755

    Contact details of provider:
    Web page: http://www.worldscinet.com/ijtaf/ijtaf.shtml

    Order Information:
    Email:

    Related research

    Keywords: Compatible bond-stock market; common equivalent martingale measure (CEMM); variance-optimal martingale (VOM); measure-valued strategy;

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    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:wsi:ijtafx:v:14:y:2011:i:05:p:723-755. 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: (Tai Tone Lim).

    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.