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Bentahar, Imen
Bouchard, Bruno
Year of Publication: 
Series/Report no.: 
SFB 649 discussion paper 2006,022
We study the problem of finding the minimal initial capital needed in order to hedge without risk a barrier option when the vector of proportions of wealth invested in each risky asset is constraint to lie in a closed convex domain. In the context of a Brownian diffusion model, we provide a PDE characterization of the super-hedging price. This extends the result of Broadie, Cvitanic and Soner (1998) and Cvitanic, Pham and Touzi (1999) which was obtained for plain vanilla options, and provides a natural numerical procedure for computing the corresponding super-hedging price. As a by-product, we obtain a comparison theorem for a class of parabolic PDE with relaxed Dirichet conditions involving a constraint on the gradient.
barrier options
portfolio constraints
viscosity solutions
Document Type: 
Working Paper

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