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

Hedging American contingent claims with constrained portfolios


Author Info

  • Ioannis Karatzas

    (Departments of Mathematics and Statistics, Columbia University, New York, NY 10027, USA)

  • (*), S. G. Kou

    (Department of Statistics, University of Michigan, Mason Hall, Ann Arbor, MI 48109-1027, USA Manuscript)

Registered author(s):


    The valuation theory for American Contingent Claims, due to Bensoussan (1984) and Karatzas (1988), is extended to deal with constraints on portfolio choice, including incomplete markets and borrowing/short-selling constraints, or with different interest rates for borrowing and lending. In the unconstrained case, the classical theory provides a single arbitrage-free price $u_0$; this is expressed as the supremum, over all stopping times, of the claim's expected discounted value under the equivalent martingale measure. In the presence of constraints, $\{u_0\}$ is replaced by an entire interval $[h_{\rm low}, h_{\rm up}]$ of arbitrage-free prices, with endpoints characterized as $h_{\rm low} = \inf_{\nu\in{\cal D}} u_\nu, h_{\rm up} = \sup_{\nu\in{\cal D}} u_\nu$. Here $u_\nu$ is the analogue of $u_0$, the arbitrage-free price with unconstrained portfolios, in an auxiliary market model ${\cal M}_\nu$; and the family $\{{\cal M}_\nu\}_{\nu\in{\cal D}}$ is suitably chosen, to contain the original model and to reflect the constraints on portfolios. For several such constraints, explicit computations of the endpoints are carried out in the case of the American call-option. The analysis involves novel results in martingale theory (including simultaneous Doob-Meyer decompositions), optimal stopping and stochastic control problems, stochastic games, and uses tools from convex analysis.

    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:
    Download Restriction: Access to the full text of the articles in this series is restricted

    File URL:
    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): 2 (1998)
    Issue (Month): 3 ()
    Pages: 215-258

    as in new window
    Handle: RePEc:spr:finsto:v:2:y:1998:i:3:p:215-258

    Note: received: July 1996; final version received: November 1996
    Contact details of provider:
    Web page:

    Order Information:

    Related research

    Keywords: Contingent claims; hedging; pricing; arbitrage; constrained markets; incomplete markets; different interest rates; Black-Scholes formula; optimal stopping; free boundary; stochastic control; stochastic games; equivalent martingale measures; simultaneous Doob-Meyer decompositions.;

    Find related papers by JEL classification:


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


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

    Cited by:
    1. Erhan Bayraktar & Yu-Jui Huang, 2010. "On the Multi-Dimensional Controller and Stopper Games," Papers 1009.0932,, revised Jan 2013.
    2. Tatjana Chudjakow & Jörg Vorbrink, 2009. "Exercise Strategies for American Exotic Options under Ambiguity," Working Papers 421, Bielefeld University, Center for Mathematical Economics.
    3. Karatzas, Ioannis & Ocone, Daniel, 2002. "A leavable bounded-velocity stochastic control problem," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 31-51, May.
    4. Erhan Bayraktar & Zhou Zhou, 2012. "On controller-stopper problems with jumps and their applications to indifference pricing of American options," Papers 1212.4894,, revised Nov 2013.
    5. Frederik Herzberg & Frank Riedel, 2012. "Existence of Financial Equilibria in Continuous Time with Potentially Complete Markets," Papers 1207.2010,
    6. Erhan Bayraktar & Song Yao, 2013. "On the Robust Optimal Stopping Problem," Papers 1301.0091,, revised Jul 2014.
    7. Zhou, Qing & Wu, Weixing & Wang, Zengwu, 2008. "Cooperative hedging with a higher interest rate for borrowing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 609-616, April.
    8. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742 Elsevier.
    9. 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.
    10. Aliprantis, Charalambos D. & Polyrakis, Yiannis A. & Tourky, Rabee, 2002. "The cheapest hedge," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 269-295, July.
    11. M. Pınar & A. Camcı, 2012. "An Integer Programming Model for Pricing American Contingent Claims under Transaction Costs," Computational Economics, Society for Computational Economics, vol. 39(1), pages 1-12, January.
    12. Erhan Bayraktar & Arash Fahim, 2011. "A Stochastic Approximation for Fully Nonlinear Free Boundary Parabolic Problems," Papers 1109.5752,, revised Nov 2013.
    13. Haluk Yener, 2012. "Maximising Survival, Growth, and Goal Reaching Under Borrowing Constraints," Papers 1209.6385,
    14. Kuhn, Christoph, 2002. "Pricing contingent claims in incomplete markets when the holder can choose among different payoffs," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 215-233, October.
    15. Xiongfei Jian & Xun Li & Fahuai Yi, 2014. "Optimal Investment with Stopping in Finite Horizon," Papers 1406.6940,
    16. Henderson, Vicky & Hobson, David, 2007. "Horizon-unbiased utility functions," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1621-1641, November.
    17. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758,


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


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:spr:finsto:v:2:y:1998:i:3:p:215-258. 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.