Let X be a locally bounded semimartingale. Using the theory of \textit{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 $q\downarrow 1$ under the assumption that X is continuous and that the density process of some equivalent martingale measure satisfies a reverse $\mathit{LLogL}$\small -inequality.
@article{1029867119,
author = {Grandits, Peter and Rheinl\"ander, Thorsten},
title = {On the minimal entropy martingale measure},
journal = {Ann. Probab.},
volume = {30},
number = {1},
year = {2002},
pages = { 1003-1038},
language = {en},
url = {http://dml.mathdoc.fr/item/1029867119}
}
Grandits, Peter; Rheinländer, Thorsten. On the minimal entropy martingale measure. Ann. Probab., Tome 30 (2002) no. 1, pp. 1003-1038. http://gdmltest.u-ga.fr/item/1029867119/