On the minimal martingale measure and the möllmer-schweizer decomposition

We provide three characterizations of the minimal martingale measure[Pcirc] associated to a given d-dimensional semimartingale X. In each case, [Pcirc] 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 Föllmer-Schweizer decomposition to the case where X is continuous, but multidimensional.