On multigrid for linear complementarity problems with application to American-style options. (English) Zbl 1031.65072
Summary: We discuss a nonlinear multigrid method for a linear complementarity problem. The convergence is improved by a recombination of iterants. The problem under consideration deals with option pricing from mathematical finance. Linear complementarity problems arise from so-called American-style options. A 2D convectiondiffusion type operator is discretized with the help of second order upwind discretizations. The properties of smoothers are analyzed with Fourier two-grid analysis. Numerical solutions obtained for the option pricing problem are compared with reference results.
MSC:
| 65K05 | Numerical mathematical programming methods |
| 35K15 | Initial value problems for second-order parabolic equations |
| 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 |
| 65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
| 91B24 | Microeconomic theory (price theory and economic markets) |
| 91G60 | Numerical methods (including Monte Carlo methods) |
