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Barrier option hedging under constraints: a viscosity approach

Abstract : 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.
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Contributor : Bruno Bouchard <>
Submitted on : Tuesday, February 28, 2006 - 8:31:22 PM
Last modification on : Monday, December 28, 2020 - 10:22:04 AM
Long-term archiving on: : Wednesday, September 8, 2010 - 3:26:12 PM


  • HAL Id : hal-00019886, version 1


Bruno Bouchard, Imen Bentahar. Barrier option hedging under constraints: a viscosity approach. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2008, 47 (4), pp.1785-1813. ⟨hal-00019886⟩



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