  In this paper we investigate the local risk-minimization approach for a
semimartingale financial market where there are restrictions on the available
information to agents who can observe at least the asset prices. We
characterize the optimal strategy in terms of suitable decompositions of a
given contingent claim, with respect to a filtration representing the
information level, even in presence of jumps. Finally, we discuss some
practical examples in a Markovian framework and show that the computation of
the optimal strategy leads to filtering problems under the real-world
probability measure and under the minimalmartingale measure.
