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The numeraire portfolio for unbounded semimartingales

Dirk Becherer (becherer@math.tu-berlin.de)
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Dirk Becherer: Technische Universität Berlin, Mathematik, MA 7-4, Str. des 17. Juni 136, 10623 Berlin, Germany Manuscript

Finance and Stochastics, 2001, vol. 5, issue 3, 327-341

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.

Keywords: Numeraire portfolio; change of numeraire; martingale measures; growth optimal portfolio; relative entropy (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Date: 2001-07-12
Note: received: March 1999; final version received: July 2000
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Citations: View citations in EconPapers (79)

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