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A Counterexample Concerning the Variance-Optimal Martingale Measure

Ales Cerny
Cass Business School

Jan Kallsen
Munich University of Technology

October 16, 2006

Cass Business School Research Paper

Abstract:
The present note addresses an open question concerning a sufficient characterization of the variance-optimal martingale measure. Denote by S the discounted price process of an asset and suppose that Q* is an equivalent martingale measure whose density is a multiple of 1 − \varphi S_T for some S-integrable process \varphi. We show that Q* does not necessarily coincide with the variance-optimal martingale measure, not even if \varphi S is a uniformly integrable Q*-martingale.

Keywords: variance-optimal martingale measure, duality, counterexample

JEL Classifications: G11, G12, C61

Working Paper Series

Date posted: July 03, 2006 ; Last revised: December 04, 2006

Suggested Citation

Cerny, Ales and Kallsen, Jan, A Counterexample Concerning the Variance-Optimal Martingale Measure (October 16, 2006). Cass Business School Research Paper. Available at SSRN: http://ssrn.com/abstract=912952

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Contact Information

Ales Cerny (Contact Author) Cass Business School ( email ) Faculty of Finance 106 Bunhill Row London United Kingdom HOME PAGE: http://www.martingales.info/
Jan Kallsen Munich University of Technology ( email ) Arcisstrasse 21 80333 Munich 80333 Germany