Before revision:  In the market consisting of one riskless bond and one risky asset, we obtain a type of the super-hedging result for some workable contingent claims . Based on this characterization of the working space, the existence and uniqueness of the optimal solution for the utility maximization problem are established using the convex duality analysis.
After revision:  In the market consisting of one riskless bond and one risky asset, we obtain a type of the super-hedging result for some workable contingent claims . Based on this characterization of the primal space, the existence and uniqueness of the optimal solution for the utility maximization problem are established using the convex duality analysis.