2006-03-30Buch DOI: 10.18452/3952
Barrier Option Hedging under Constraints
A Viscosity Approach
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.
Dateien zu dieser Publikation
Is Part Of Series: Sonderforschungsbereich 649: Ökonomisches Risiko - 22, SFB 649 Papers, ISSN:1860-5664