Advanced Search
MyIDEAS: Login

Weighted norm inequalities and hedging in incomplete markets

Contents:

Author Info

  • Martin Schweizer

    (TU Berlin, Fachbereich Mathematik, Strasse des 17. Juni 136, D-10623 Berlin, Germany)

  • Christophe Stricker

    (Laboratoire de Mathématiques, URA CNRS 741, 16 Route de Gray, F-25030 Besançon Cedex, France)

  • Freddy Delbaen

    (Department of Mathematics, Eidgenössische Technische Hochschule Zürich, CH-8092 Zürich, Switzerland)

  • Pascale Monat

    (Laboratoire de Mathématiques, URA CNRS 741, 16 Route de Gray, F-25030 Besançon Cedex, France)

  • Walter Schachermayer

    (Universität Wien, Brünnerstrasse 72, A-1210 Wien, Austria)

Registered author(s):

    Abstract

    Let $X$ be an ${\Bbb R}^d$-valued special semimartingale on a probability space $(\Omega , {\cal F} , ({\cal F} _t)_{0 \leq t \leq T} ,P)$ with canonical decomposition $X=X_0+M+A$. Denote by $G_T(\Theta )$ the space of all random variables $(\theta \cdot X)_T$, where $\theta $ is a predictable $X$-integrable process such that the stochastic integral $\theta \cdot X$ is in the space ${\cal S} ^2$ of semimartingales. We investigate under which conditions on the semimartingale $X$ the space $G_T(\Theta )$ is closed in ${\cal L} ^2(\Omega , {\cal F} ,P)$, a question which arises naturally in the applications to financial mathematics. Our main results give necessary and/or sufficient conditions for the closedness of $G_T(\Theta )$ in ${\cal L} ^2(P)$. Most of these conditions deal with BMO-martingales and reverse Hölder inequalities which are equivalent to weighted norm inequalities. By means of these last inequalities, we also extend previous results on the Föllmer-Schweizer decomposition.

    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://link.springer.de/link/service/journals/00780/papers/7001003/70010181.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted

    File URL: http://link.springer.de/link/service/journals/00780/papers/7001003/70010181.ps.gz
    Download Restriction: Access to the full text of the articles in this series is restricted

    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 Springer in its journal Finance and Stochastics.

    Volume (Year): 1 (1997)
    Issue (Month): 3 ()
    Pages: 181-227

    as in new window
    Handle: RePEc:spr:finsto:v:1:y:1997:i:3:p:181-227

    Note: received: January 1996; final version received: April 1996
    Contact details of provider:
    Web page: http://www.springerlink.com/content/101164/

    Order Information:
    Web: http://link.springer.de/orders.htm

    Related research

    Keywords: Semimartingales; stochastic integrals; reverse Hölder inequalities;

    Find related papers by JEL classification:

    References

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

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as in new window

    Cited by:
    1. Arai, Takuji, 2005. "Some properties of the variance-optimal martingale measure for discontinuous semimartingales," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 163-170, September.
    2. Michael Kohlmann & Shanjian Tang, 2000. "Global Adapted Solution of One-Dimensional Backward Stochastic Riccati Equations, with Application to the Mean-Variance Hedging," CoFE Discussion Paper 00-26, Center of Finance and Econometrics, University of Konstanz.
    3. Bayraktar, Erhan & Kravitz, Ross, 2013. "Stability of exponential utility maximization with respect to market perturbations," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1671-1690.
    4. Badescu, Alexandru M. & Kulperger, Reg J., 2008. "GARCH option pricing: A semiparametric approach," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 69-84, August.
    5. Stephane Goutte & Armand Ngoupeyou, 2012. "Optimization problem and mean variance hedging on defaultable claims," Papers 1209.5953, arXiv.org.
    6. M. Mania & R. Tevzadze & T. Toronjadze, 2007. "$L^2$-approximating pricing under restricted information," Papers 0708.4095, arXiv.org.
    7. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2003. "A Comparison of q-optimal Option Prices in a Stochastic Volatility Model with Correlation," OFRC Working Papers Series 2003mf02, Oxford Financial Research Centre.
    8. Schweizer, Martin, 2001. "From actuarial to financial valuation principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 31-47, February.
    9. Christoph Czichowsky, 2013. "Time-consistent mean-variance portfolio selection in discrete and continuous time," Finance and Stochastics, Springer, vol. 17(2), pages 227-271, April.
    10. Choulli, Tahir & Vandaele, Nele & Vanmaele, Michèle, 2010. "The Föllmer-Schweizer decomposition: Comparison and description," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 853-872, June.
    11. M. Mania & R. Tevzadze & T. Toronjadze, 2007. "Mean-variance Hedging Under Partial Information," Papers math/0703424, arXiv.org.
    12. Vicky Henderson, 2002. "Analytical Comparisons of Option prices in Stochastic Volatility Models," OFRC Working Papers Series 2002mf03, Oxford Financial Research Centre.
    13. Jianming Xia, 2006. "Mean-variance Hedging in the Discontinuous Case," Papers math/0607775, arXiv.org.
    14. Ke Du & Eckhard Platen, 2011. "Three-Benchmarked Risk Minimization for Jump Diffusion Markets," Research Paper Series 296, Quantitative Finance Research Centre, University of Technology, Sydney.

    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:spr:finsto:v:1:y:1997:i:3:p:181-227. 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: (Guenther Eichhorn) or (Christopher F Baum).

    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.