Local risk-minimization under restricted information on asset prices

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 an application to 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 minimal martingale measure.