On the minimal entropy martingale measure

Let X be a locally bounded semimartingale. Using the theory of BMO-martingales we give a sufficient criterion for a martingale measure for X to minimize relative entropy among all martingale measures. This is applied to prove convergence of the q-optimal martingale measure to the minimal entropy martingale measure in entropy for q ↓ 1 under the assumption that X is continuous and that the density process of some equivalent martingale measure satisfies a reverse LLogL-inequality.

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