Consistent Market Extensions under the Benchmark Approach

Damir Filipovic and Eckhard Platen ()
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Damir Filipovic: Department of Mathematics, University of Munich

No 189, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: The existence of the growth optimal portfolio (GOP), also known as Kelly portfolio, is vital for a financial market to be meaningful. The GOP, if it exists, is uniquely determined by the market parameters of the primary security accounts. However, markets may develop and new security accounts become tradable. What happens to the GOP if the original market is extended? In this paper we provide a complete characterization of market extensions which are consistent with the existence of a GOP. We show that a three fund separation theorem applies for the extended GOP. This includes, in particular, the introduction of a locally risk free security, the savings account. We give necessary and sufficient conditions for a consistent exogenous specification of the prevailing short rates.

Keywords: growth optimal portfolio; market extension; three fund seperation theorem (search for similar items in EconPapers)
Pages: 13 pages
Date: 2007-01-01
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Citations: View citations in EconPapers (1)

Published as: Filipovic, D. and Platen, E., 2009, "Consistent Market Extensions under the Benchmark Approach", Mathematical Finance, 19(1), 41-52.

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https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp189.pdf (application/pdf)

Related works:
Journal Article: CONSISTENT MARKET EXTENSIONS UNDER THE BENCHMARK APPROACH (2009)
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