IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v10y2003i3p215-228.html
   My bibliography  Save this article

On parabolic equations with gauge function term and applications to the multidimensional Leland equation

Author

Listed:
  • Jorg Kampen
  • Marco Avellaneda

Abstract

Sufficient conditions for existence and a closed form probabilistic representation are obtained for solutions of nonlinear parabolic equations with gauge function term. In particular, the result applies to the generalized Leland equationwhere BSn is the n-dimensional Black-Scholes operator, Ai are positive transaction cost numbers, ρjk are the correlations between returns of asset Sj and asset Sk and DSrkV is an abbreviation of along with the volatilities σr of the rth asset Sr. It is shown that the associated Cauchy problem has a solution for uniformily bounded continuous data if for all i, j, i≠j 0≤Ai<1 and [image omitted] [image omitted]Comment is made on the existence, as Ai→1 for some i, of small and large correlations between returns of assets.

Suggested Citation

  • Jorg Kampen & Marco Avellaneda, 2003. "On parabolic equations with gauge function term and applications to the multidimensional Leland equation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(3), pages 215-228.
  • Handle: RePEc:taf:apmtfi:v:10:y:2003:i:3:p:215-228 DOI: 10.1080/1350486032000107361
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000107361
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    4. NESTEROV , Yurii & TODD , Michael, 1995. "Primal-Dual Interior-Point Methods for Self-Scaled Cones," CORE Discussion Papers 1995044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    8. Klaus Sandmann & Dieter Sondermann, 1997. "A Note on the Stability of Lognormal Interest Rate Models and the Pricing of Eurodollar Futures," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 119-125.
    9. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
    Full references (including those not matched with items on IDEAS)

    More about this item

    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:taf:apmtfi:v:10:y:2003:i:3:p:215-228. 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: (Chris Longhurst). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    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.

    We have no references for this item. You can help adding them by using 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.