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Barrier option hedging under constraints: a viscosity approach

Bouchard, Bruno; Ben Tahar, Imen (2006), Barrier option hedging under constraints: a viscosity approach, SIAM Journal on Control and Optimization, 45, 5, p. 1846-1874. http://dx.doi.org/10.1137/06065324X

Type
Article accepté pour publication ou publié
Date
2006
Journal name
SIAM Journal on Control and Optimization
Volume
45
Number
5
Publisher
Society for Industrial and Applied Mathematics
Pages
1846-1874
Publication identifier
http://dx.doi.org/10.1137/06065324X
Metadata
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Author(s)
Bouchard, Bruno
Ben Tahar, Imen
Abstract (EN)
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 constrained to lie in a closed convex domain. In the context of a Brownian diffusion model, we provide a PDE characterization of the superhedging price. This extends the result of Broadie, Cvitani` c, and Soner [Rev. Financial Stud., 11 (1998), pp. 59–79] and Cvitani` c, Pham, and Touzi [J. Appl. Probab., 36 (1999), pp. 523–545] which was obtained for plain vanilla options and provides a natural numerical procedure for computing the corresponding superhedging price. As a by-product, we obtain a comparison theorem for a class of parabolic PDEs with relaxed Dirichlet conditions involving a constraint on the gradient.
Subjects / Keywords
viscosity solutions; portfolio constraints; Mathematical Finance
JEL
G10 - General

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