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· S T 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.
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Černý et al. (2008) studied this question.
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