The mean-variance hedging of a defaultable option with partial information

We consider the mean-variance hedging of a defaultable claim in a general stochastic volatility model. By introducing a new measure Q(0), we derive the martingale representation theorem with respect to the investors' filtration G. We present an explicit form of the optimal-variance martingale measure by means of a stochastic Riccati equation (SRE). For a general contingent claim, we represent the optimal strategy and the optimal cost of the mean-variance hedging by means of another backward stochastic differential equation (BSDE). For the defaultable option, especially when there exists a random recovery rate we give an explicit form of the solution of the BSDE.