A COUNTEREXAMPLE CONCERNING THE VARIANCE‐OPTIMAL MARTINGALE MEASURE

Aleš Černý and Jan Kallsen

Mathematical Finance, 2008, vol. 18, issue 2, 305-316

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 −ϕ·ST for some S‐integrable process ϕ. We show that Q★ does not necessarily coincide with the variance‐optimal martingale measure, not even if ϕ·S is a uniformly integrable Q★‐martingale.

Date: 2008
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