In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. Starting with an amount of money smaller than the superhedging price of the claim, we want to find a strategy that minimizes the risk of a shortfall. We use a convex risk measure. This problem can be split into a static optimization problem and a representation problem. We show that the optimal strategy consists in superhedging a modified claim whose payoff is the product of the solution of the static problem and the original payoff. To solve the static problem we apply convex duality methods. We provide necessary and sufficient optimality conditions. ( Slides)
Speaker: Birgit Rudloff, Princeton University