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The numeraire portfolio for unbounded semimartingales

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  • Dirk Becherer

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

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    Abstract

    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.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 5 (2001)
    Issue (Month): 3 ()
    Pages: 327-341

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    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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    Related research

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

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