Consistent Market Extensions under the Benchmark Approach

12 Pages Posted: 17 Jan 2009

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group; University of Technology Sydney, School of Mathematical and Physical Sciences; Financial Research Network (FIRN)

Date Written: 2007-08

Abstract

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.

Suggested Citation

Filipovic, Damir and Platen, Eckhard, Consistent Market Extensions under the Benchmark Approach (2007-08). Mathematical Finance, Vol. 19, Issue 1, pp. 41-52, January 2009. Available at SSRN: https://ssrn.com/abstract=1327435 or http://dx.doi.org/10.1111/j.1467-9965.2008.00356.x

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group ( email )

Broadway
GPO Box 123
Sydney, NSW 2007, 2007
Australia
+61 2 9514 7759 (Phone)

HOME PAGE: http://datasearch.uts.edu.au/business/finance/staff/StaffDetails.cfm?UnitStaffId=90

University of Technology Sydney, School of Mathematical and Physical Sciences ( email )

P.O. Box 123
Broadway
Sydney, New South Wales 2007
Australia
+61 (02) 9514 2271 (Phone)

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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