Consistent Market Extensions under the Benchmark Approach

The existence of the growth optimal portfolio (GOP), also known as the 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.


Published in:
Mathematical Finance, 19, 1, 41-52
Year:
2009
Publisher:
Wiley-Blackwell
ISSN:
0960-1627
Laboratories:




 Record created 2010-04-27, last modified 2018-01-28


Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)