NUMERICAL APPROXIMATION FOR A SUPERREPLICATION PROBLEM UNDER GAMMA CONSTRAINTS.

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. [ABSTRACT FROM AUTHOR]