Barrier option hedging under constraints: a viscosity approach

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 649 Discussion Paper ; No. 2006,022

Classification and Topics

• Classification: Wirtschaft
• Subject: Super-replication ; barrier options ; portfolio constraints ; viscosity solutions

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Bentahar, Imen ; Bouchard, Bruno
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (where): Berlin
• (when): 2006

Further information

• Handle: http://hdl.handle.net/10419/25105
• Last update: 10.03.2025, 11:44 AM CET