Solving the problem of partial hedging through a dual problem

In this paper we consider the problem of partial hedging studied in [20]. In this problem, the risk of shortfall is estimated using a robust convex loss functional $L(\cdot)$. In our work, we formulate a dual problem different from the dual problem in [20], we prove the absence of a duality gap, and also the existence of a solution to the primal and dual problems. In addition, we obtain the results of [20] under weaker assumptions using an approach related to the application of theorems of convex analysis.