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The numeraire portfolio for unbounded semimartingales


  • Dirk Becherer

    () (Technische Universit├Ąt Berlin, Mathematik, MA 7-4, Str. des 17. Juni 136, 10623 Berlin, Germany Manuscript)


Asset prices discounted by a tradable numeraire N should be (local) martingales under some measure Q that is equivalent to the original probability measure P. Instead of studying the set of equivalent martingale measures with respect to a prespecified numeraire, we will look for a tradable numeraire $N^P$ such that the discounted asset prices become martingales with respect to the original measure P. $N^P$ is called (P-)numeraire portfolio. Since the above martingale condition is too stringent to obtain a general existence result, we define a (generalized) numeraire portfolio by a weaker requirement. This $N^P$ is characterized as the solution to several optimization problems.

Suggested Citation

  • Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
  • Handle: RePEc:spr:finsto:v:5:y:2001:i:3:p:327-341
    Note: received: March 1999; final version received: July 2000

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    More about this item


    Numeraire portfolio; change of numeraire; martingale measures; growth optimal portfolio; relative entropy;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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