Optional decomposition and Lagrange multipliers

Author Info

• 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.

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.

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): 2 (1997)
Issue (Month): 1 ()
Pages: 69-81

as in new window
Handle: RePEc:spr:finsto:v:2:y:1997:i:1:p:69-81

Contact details of provider:

Order Information:

Related research

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

Other versions of this item:

Find related papers by 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

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. 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 in new window

Cited by:
1. 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.
2. 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.
3. Jun Sekine, 2012. "Long-term optimal portfolios with floor," Finance and Stochastics, Springer, vol. 16(3), pages 369-401, July.
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. 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.
6. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
7. Frank Riedel, 2007. "Optimal stopping under ambiguity," Working Papers 390, Bielefeld University, Center for Mathematical Economics.
8. Hans F\"ollmer & Alexander Schied, 2013. "Probabilistic aspects of finance," Papers 1309.7759, arXiv.org.
9. Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Corrections

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: (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.