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- Title
Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation.
- Authors
WANG, S.; YANG, X. Q.; TEO, K. L.
- Abstract
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.
- Subjects
LINEAR complementarity problem; MATRICES (Mathematics); MATHEMATICAL programming; PARABOLIC differential equations; VECTOR algebra; MATHEMATICAL optimization; PARTIAL differential equations; OPERATIONS research; FUNCTIONAL equations
- Publication
Journal of Optimization Theory & Applications, 2006, Vol 129, Issue 2, p227
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-006-9062-3