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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
1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LJLL - Laboratoire Jacques-Louis Lions
3 TOSCA
CNRS - Centre National de la Recherche Scientifique : UMR7502, INPL - Institut National Polytechnique de Lorraine, Université Nancy 2, UHP - Université Henri Poincaré - Nancy 1, CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Lorraine
4 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
5 OC - Optimisation et commande
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.
Keywords : generalized finite difference scheme viscosity solution numerical approximation Super-replication problem Howard's algorithm monotone scheme
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https://hal.archives-ouvertes.fr/hal-00278077
Contributor : Olivier Bokanowski Connect in order to contact the contributor
Submitted on : Sunday, May 11, 2008 - 3:13:22 AM
Last modification on : Wednesday, May 11, 2022 - 12:06:06 PM
Long-term archiving on: : Friday, May 28, 2010 - 6:50:02 PM

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CNRS | INRIA | IECN | INSMI | X-CMAP | X | UPMC | CMAP | ENSTA | INRIA2 | TDS-MACS | UNIV-LORRAINE | PMA | X-DEP-MATHA | SORBONNE-UNIVERSITE | SU-SCIENCES | UNIV-PARIS7 | UNIV-PARIS | SU-TI | LJLL | LPSM

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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, 47 (3), pp.2289-2320. ⟨10.1137/080725222⟩. ⟨hal-00278077⟩

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