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Numerical approximation for a superreplication problem under gamma constraints

Benjamin Bruder 1 Olivier Bokanowski 2 Stefania Maroso 3, 4 Hasnaa Zidani 4, 5
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
4 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : We study a superreplication problem of European options with gamma constraints, in mathematical finance. The initially unbounded control problem is set back to a problem involving a viscosity PDE solution with a set of bounded controls. Then a numerical approach is introduced, inconditionnally stable with respect to the mesh steps. A generalized finite difference scheme is used since basic finite differences cannot work in our case. Numerical tests illustrate the validity of our approach.
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Contributor : Olivier Bokanowski <>
Submitted on : Sunday, May 11, 2008 - 3:13:22 AM
Last modification on : Friday, March 27, 2020 - 4:04:43 AM
Long-term archiving on: : Friday, May 28, 2010 - 6:50:02 PM


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  • HAL Id : hal-00278077, version 1


Benjamin Bruder, Olivier Bokanowski, Stefania Maroso, Hasnaa Zidani. Numerical approximation for a superreplication problem under gamma constraints. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2009, 3 (47), pp.2289-2320. ⟨hal-00278077⟩



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