Abstract
In this presentation, we are interested in the super replication of European claims under Delta convex constraints in multi-dimensional local volatility models. The corresponding super-replication price of a given claim has been widely studied in the literature and its terminal value which dominates the claim of interest is the so-called facelift transform of the claim. We investigate under which conditions the super replication price and strategy of any claim coincides with the exact replication price and strategy of the facelift transform of this claim. We exhibit a necessary and sufficient geometric condition for this property, which combines the dynamics of the stock together with the characteristics of the polyhedral convex set of constraints.
The obtention of this condition relies on the use of first order viability properties for linear parabolic PDEs. We investigate in details several practical cases of interest, such as multidimensional Black Scholes model, non-tradable assets, no short selling restrictions or diversification requirements.
Joint work with R. Elie and I Kharroubi (Universite Paris Dauphine)