Before revision:  We characterize the optimal  strategy in terms of the integrand in the Galtchouk-Kunita-Watanabe decomposition of the defaultable claim with respect to the minimal martingale measure and the available information flow.
After revision:  We characterize the optimal hedging strategy in terms of the integrand in the Galtchouk-Kunita-Watanabe decomposition of the defaultable claim with respect to the minimal martingale measure and the available information flow.