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

Abstract

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.