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The numeraire portfolio for unbounded semimartingales

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Author Info
Dirk Becherer () (Technische Universität Berlin, Mathematik, MA 7-4, Str. des 17. Juni 136, 10623 Berlin, Germany Manuscript)
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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Publisher 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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Find related papers by 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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  2. Constantinos Kardaras, 2009. "Num\'eraire-invariant preferences in financial modeling," Quantitative Finance Papers 0903.3736, arXiv.org, revised Nov 2009. [Downloadable!]
  3. Eckhard Platen & Jason West, 2004. "A Fair Pricing Approach to Weather Derivatives," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 23-53, March. [Downloadable!] (restricted)
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  11. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Research Paper Series 129, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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  13. Ralf Korn & Frank Oertel & Manfred Schäl, 2003. "Notes and Comments: The numeraire portfolio in financial markets modeled by a multi-dimensional jump diffusion process," Decisions in Economics and Finance, Springer, vol. 26(2), pages 153-166, November. [Downloadable!] (restricted)
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  16. Dmitry Rokhlin, 2008. "Asymptotic arbitrage and numéraire portfolios in large financial markets," Finance and Stochastics, Springer, vol. 12(2), pages 173-194, April. [Downloadable!] (restricted)
  17. Constantinos Kardaras, 2008. "No-Free-Lunch equivalences for exponential Levy models," Quantitative Finance Papers 0803.2169, arXiv.org. [Downloadable!]
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