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A splitting method for fully nonlinear degenerate parabolic PDEs. (English) Zbl 1282.65103

The author proposes a splitting scheme for fully nonlinear degenerate parabolic partial differential equations (PDEs) which is motivated by various applications in Asian price option or optimal commodity trading. The method proposed uses a probabilistic scheme to deal with the non-degenerate part together with a semi-Lagrangean scheme for the degenerate part. Under reasonable conditions is obtained the general convergence of the scheme is obtained. Numerical experiment are also presented to support the theoretical findings.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65C05 Monte Carlo methods
35K65 Degenerate parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
91B24 Microeconomic theory (price theory and economic markets)
91G60 Numerical methods (including Monte Carlo methods)
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