A counterexample concerning the variance-optimal martingale measure

@inproceedings{Cern2006ACC,
  title={A counterexample concerning the variance-optimal martingale measure},
  author={Ales Cern{\'y} and Jan Kallsen},
  year={2006}
}
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. 

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