Before revision:   Since the minimal martingale measure fails to produce a probability measure in this setting, we construct local risk minimization hedging strategies with respect to a risk neutral measure. Local risk minimization is investigated in the context of Gaussian driven models, and two other minimum variance hedges are proposed in order to extend Duan's delta hedge.
After revision:  Since the minimal martingale measure fails to produce a probability measure in this setting, we construct local risk minimization hedging strategies with respect to a pricing kernel. These approaches are investigated in the context of Gaussian driven models, and two other minimum variance hedges are proposed in order to extend Duan's delta hedge.