Direct Characterization of the Value of Super-Replication under Stochastic Volatility and Portfolio Constraints.

We study the problem of minimal initial capital needed in order to hedge a European contengent claim without risk. The financial market presents incompleteness arising from two sources: stochastic volatility and portfolio constraints described by a closed convex set. In contrast with previous literature which uses the dual formulation of the problem, we usean original dynamic programming principle stated directly on the initial problem, as in Soner and Touzi.