Advanced Search
MyIDEAS: Login to save this paper or follow this series

Integral representation of martingales motivated by the problem of endogenous completeness in financial economics

Contents:

Author Info

  • Dmitry Kramkov

    (Carnegie Mellon and Oxford)

  • Silviu Predoiu

    (Citigroup)

Registered author(s):

    Abstract

    Let $\mathbb{Q}$ and $\mathbb{P}$ be equivalent probability measures and let $\psi$ be a $J$-dimensional vector of random variables such that $\frac{d\mathbb{Q}}{d\mathbb{P}}$ and $\psi$ are defined in terms of a weak solution $X$ to a $d$-dimensional stochastic differential equation. Motivated by the problem of \emph{endogenous completeness} in financial economics we present conditions which guarantee that every local martingale under $\mathbb{Q}$ is a stochastic integral with respect to the $J$-dimensional martingale $S_t \set \mathbb{E}^{\mathbb{Q}}[\psi|\mathcal{F}_t]$. While the drift $b=b(t,x)$ and the volatility $\sigma = \sigma(t,x)$ coefficients for $X$ need to have only minimal regularity properties with respect to $x$, they are assumed to be analytic functions with respect to $t$. We provide a counter-example showing that this $t$-analyticity assumption for $\sigma$ cannot be removed.

    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://arxiv.org/pdf/1110.3248
    File Function: Latest version
    Download Restriction: no

    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1110.3248.

    as in new window
    Length:
    Date of creation: Oct 2011
    Date of revision: Oct 2012
    Publication status: Published in Stochastic Processes and their Applications, 124 (1), pages 81-100, 2014
    Handle: RePEc:arx:papers:1110.3248

    Contact details of provider:
    Web page: http://arxiv.org/

    Related research

    Keywords:

    This paper has been announced in the following NEP Reports:

    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. Julien HUGONNIER & Semyon MALAMUD & Eugene TRUBOWITZ, . "Endogenous completeness of diffusion driven equilibrium markets," Swiss Finance Institute Research Paper Series, Swiss Finance Institute 09-41, Swiss Finance Institute.
    2. Frederik Herzberg & Frank Riedel, 2012. "Existence of Financial Equilibria in Continuous Time with Potentially Complete Markets," Papers 1207.2010, arXiv.org.
    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:arx:papers:1110.3248. 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: (arXiv administrators).

    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.