Consistent Market Extensions under the Benchmark Approach
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.
|Date of creation:||01 Jan 2007|
|Date of revision:|
|Publication status:||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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- Eckhard Platen, 2006.
"A Benchmark Approach To Finance,"
Wiley Blackwell, vol. 16(1), pages 131-151.
- Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
- Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
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