Weighted norm inequalities and hedging in incomplete markets

Let be an -valued special semimartingale on a probability space with canonical decomposition . Denote by the space of all random variables , where is a predictable -integrable process such that the stochastic integral is in the space of semimartingales. We investigate under which conditions on the semimartingale the space is closed in , a question which arises naturally in the applications to financial mathematics. Our main results give necessary and/or sufficient conditions for the closedness of in . Most of these conditions deal with BMO-martingales and reverse H?lder inequalities which are equivalent to weighted norm inequalities. By means of these last inequalities, we also extend previous results on the F?llmer-Schweizer decomposition.