Bokanowski, Olivier; Bruder, Benjamin; Maroso, Stefania; Zidani, Hasnaa Numerical approximation for a superreplication problem under gamma constraints. (English) Zbl 1190.91141 SIAM J. Numer. Anal. 47, No. 3, 2289-2320 (2009). 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. Cited in 8 Documents 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) Keywords:superreplication problem; viscosity solution; numerical approximation; generalized finite difference scheme; monotone scheme; Howard’s algorithm PDFBibTeX XMLCite \textit{O. Bokanowski} et al., SIAM J. Numer. Anal. 47, No. 3, 2289--2320 (2009; Zbl 1190.91141) Full Text: DOI