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The continuous behavior of the numeraire portfolio under small changes in information structure, probabilistic views and investment constraints

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  • Constantinos Kardaras

Abstract

The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes, when deflated by it, supermartingales. The numeraire portfolio depends on market characteristics, which include: (a) the information flow available to acting agents, given by a filtration; (b) the statistical evolution of the asset prices and, more generally, the states of nature, given by a probability measure; and (c) possible restrictions that acting agents might be facing on available investment strategies, modeled by a constraints set. In a financial market with continuous-path asset prices, we establish the stable behavior of the numeraire portfolio when each of the aforementioned market parameters is changed in an infinitesimal way.

Suggested Citation

  • Constantinos Kardaras, 2008. "The continuous behavior of the numeraire portfolio under small changes in information structure, probabilistic views and investment constraints," Papers 0804.2912, arXiv.org, revised Nov 2009.
    • Handle: RePEc:arx:papers:0804.2912
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    References listed on IDEAS

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    1. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
    2. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    3. Stefan Ankirchner & Steffen Dereich & Peter Imkeller, 2005. "The Shannon information of filtrations and the additional logarithmic utility of insiders," Papers math/0503013, arXiv.org, revised May 2006.
    4. Larsen, Kasper & Zitkovic, Gordan, 2007. "Stability of utility-maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1642-1662, November.
    5. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
    6. Constantinos Kardaras & Eckhard Platen, 2008. "On Financial Markets where only Buy-And-Hold Trading is Possible," Research Paper Series 213, Quantitative Finance Research Centre, University of Technology, Sydney.
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