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Power penalty method for a linear complementarity problem arising from American option valuation. (English) Zbl 1139.91020
Summary: In this paper, we present a power penalty function approach to the linear complementarity problem arising from pricing American options. The problem is first reformulated as a variational inequality problem; the resulting variational inequality problem is then transformed into a nonlinear parabolic partial differential equation (PDE) by adding a power penalty term. It is shown that the solution to the penalized equation converges to that of the variational inequality problem with an arbitrary order. This arbitrary-order convergence rate allows us to achieve the required accuracy of the solution with a small penalty parameter. A numerical scheme for solving the penalized nonlinear PDE is also proposed. Numerical results are given to illustrate the theoretical findings and to show the effectiveness and usefulness of the method.
91B28Finance etc. (MSC2000)
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
35K20Second order parabolic equations, initial boundary value problems
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