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Journal Articles SIAM Journal on Numerical Analysis Year : 2009

Numerical approximation for a superreplication problem under gamma constraints

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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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Dates and versions

hal-00278077 , version 1 (11-05-2008)

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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, 2009, 47 (3), pp.2289-2320. ⟨10.1137/080725222⟩. ⟨hal-00278077⟩
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