unique equivalent martingale measure in incomplete markets

[d.koutsomito]

Hello there,

Do you have any idea about how we can prove, and under which conditions, that an equivalent martingale measure (EMM) in an incomplete market is unique? The assumptions we have made are:

1) that the stochastic process St of the asset is a semi martingale (continuous) and
2) that this EMM exists.

Thanks.

 

[ygmwy]

Use Girsanov's Theorem to transform to the Q-measure, and show that multiple solutions to the transformation exist.

 

[d.koutsomito]

I think that if we use Girsanov's theorem there are cases in which the local martingale stochastic exponential is not uniformly integrable (Delbaen and Schachermayer constructed such a stochastic process). My question is that supposed we know that the optimal equivalent martingale measure is the variance optimal ( i.e. the one which minimizes the variance of the martingale measure), so its existence is granted, we want to prove that this measure is unique.