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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)
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