Download This PaperA 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
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
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