Numerical Approximation for a Superreplication Problem under Gamma Constraints | Zendy

Olivier Bokanowski | Zendy; Benjamin Bruder | Zendy; Stefania Maroso | Zendy; Hasnaa Zidani | Zendy

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Numerical Approximation for a Superreplication Problem under Gamma Constraints

Author(s) -

Olivier Bokanowski,

Benjamin Bruder,

Stefania Maroso,

Hasnaa Zidani

Publication year - 2009

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/080725222

Subject(s) - mathematics , bounded function , set (abstract data type) , scheme (mathematics) , viscosity solution , numerical analysis , finite difference scheme , finite difference , work (physics) , mathematical optimization , mathematical analysis , computer science , mechanical engineering , engineering , programming language

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, unconditionally 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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