GKW representation theorem and linear BSDEs under restricted   information. An application to risk-minimization
  In this paper we provide Galtchouk-Kunita-Watanabe representation results in the case where there are restrictions on the available information. This allows to prove existence and uniqueness for linear backward stochastic differential equations driven by a general c\`adl\`ag martingale under partial information. Furthermore, we discuss an application to risk-minimization where we extend the results of F\"ollmer and Sondermann (1986) to the partial information framework and we show how our result fits in the approach of Schweizer (1994). 
Claudia Ceci, Alessandra Cretarola and Francesco Russo
math.PR