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Numerical approximation for a superreplication problem under gamma constraints. (English) Zbl 1190.91141

Summary: 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.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
91G60 Numerical methods (including Monte Carlo methods)
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