# A Counterexample Concerning the Variance-Optimal Martingale Measure

Mathematical Finance, 2008, 18(2), 305-316

13 Pages Posted: 3 Jul 2006 Last revised: 22 Jun 2020

See all articles by Aleš Černý

## Aleš Černý

The Business School (formerly Cass), City, University of London

## Jan Kallsen

Munich University of Technology

Date Written: October 16, 2006

### 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 Classification: G11, G12, C61

Suggested Citation

Černý, Aleš and Kallsen, Jan, A Counterexample Concerning the Variance-Optimal Martingale Measure (October 16, 2006). Mathematical Finance, 2008, 18(2), 305-316, Available at SSRN: https://ssrn.com/abstract=912952 or http://dx.doi.org/10.2139/ssrn.912952