In this paper we investigate the local risk-minimization approach for a  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 the predictable covariation of the optimal value process and the stock price with respect to a given 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 solve filtering problems under the real-world probability measure and under the minimal martingale measure.
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.
A
semimartingale
R
the predictable covariation of the optimal value process and the stock price
suitable decompositions of a given contingent claim,
D
given
D
solve
R
minimal martingale
minimalmartingale