IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v2y1997i1p69-81.html
   My bibliography  Save this article

Optional decomposition and Lagrange multipliers

Author

Listed:
  • H. Föllmer

    (Institut für Mathematik, Humboldt Universität, Unter den Linden 6, D-10099 Berlin, Germany)

  • Y.M. Kabanov

    (Central Economics and Mathematics Institute of the Russian Academy of Sciences, Moscow)

Abstract

Let ${\cal Q}$ be the set of equivalent martingale measures for a given process $S$, and let $X$ be a process which is a local supermartingale with respect to any measure in ${\cal Q}$. The optional decomposition theorem for $X$ states that there exists a predictable integrand $\varphi$ such that the difference $X-\varphi\cdot S$ is a decreasing process. In this paper we give a new proof which uses techniques from stochastic calculus rather than functional analysis, and which removes any boundedness assumption.

Suggested Citation

  • H. Föllmer & Y.M. Kabanov, 1997. "Optional decomposition and Lagrange multipliers," Finance and Stochastics, Springer, vol. 2(1), pages 69-81.
  • Handle: RePEc:spr:finsto:v:2:y:1997:i:1:p:69-81
    Note: received: January 1996; final version received: June 1997
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00780/papers/7002001/70020069.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/7002001/70020069.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 below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    2. Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B 294, University of Bonn, Germany.
    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


    Cited by:

    1. Jun Sekine, 2012. "Long-term optimal portfolios with floor," Finance and Stochastics, Springer, vol. 16(3), pages 369-401, July.
    2. Alexander Chigodaev, 2016. "Recursive Method for Guaranteed Valuation of Options in Deterministic Game Theoretic Approach," HSE Working papers WP BRP 53/FE/2016, National Research University Higher School of Economics.
    3. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Bank, Peter & Riedel, Frank, 1999. "Optimal consumption choice under uncertainty with intertemporal substitution," SFB 373 Discussion Papers 1999,71, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Hans Follmer & Alexander Schied, 2013. "Probabilistic aspects of finance," Papers 1309.7759, arXiv.org.
    6. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    7. Filipovic, Damir & Kupper, Michael, 2007. "Monotone and cash-invariant convex functions and hulls," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 1-16, July.
    8. Riedel, Frank, 2010. "Optimal Stopping under Ambiguity," Center for Mathematical Economics Working Papers 390, Center for Mathematical Economics, Bielefeld University.
    9. Kohlmann, Michael & Niethammer, Christina R., 2007. "On convergence to the exponential utility problem," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1813-1834, December.
    10. Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.
    11. Matos, Joao Amaro de & Lacerda, Ana, 2004. "Dry Markets and Superreplication Bounds of American Derivatives," FEUNL Working Paper Series wp461, Universidade Nova de Lisboa, Faculdade de Economia.

    More about this item

    Keywords

    Optional decomposition; semimartingale; equivalent martingale measure; Hellinger process; Lagrange multiplier;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:finsto:v:2:y:1997:i:1:p:69-81. 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: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.