On the Minimal Martingale Measure and the Foellmer- Schweizer Decomposition

We provide three characterizations of the minimal martingale measure P associated to a given d- dimensional semimartingale X. In each case, P is shown to be the unique solution of an optimization problem where one minimizes a certain functional over a suitable class of signed local martingale measures for X. Furthermore, we extend a result of Ansel and Stricker on the Foellmer-Schweizer decomposition to the case where X is continuous, but multidimensional.