GKW representation theorem under restricted information: An application to risk-minimization

We provide Galtchouk-Kunita-Watanabe representation results in the case where there are restrictions on the available information. This allows one to prove the existence and uniqueness of solution for special equations driven by a general square integrable càdlàg martingale under partial information. Furthermore, we discuss an application to risk-minimization where we extend the results of Föllmer and Sondermann, Hedging of non-redundant contingent claims, to the partial information framework and we show how our result fits in the approach of Schweizer, Risk-minimizing hedging strategies under restricted information.