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首页> 外文期刊>Journal of Optimization Theory and Applications >Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation
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Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation

机译：美式期权估值引起的线性互补问题的幂惩罚方法

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摘要

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.
机译：在本文中，我们提出了一种针对因美式期权定价而引起的线性互补问题的幂函数函数方法。首先将该问题重新表述为变分不平等问题；然后，通过添加幂惩罚项，将所得的变分不等式问题转化为非线性抛物线偏微分方程（PDE）。结果表明，惩罚方程的解收敛于任意阶变分不等式的解。这种任意阶的收敛速度使我们能够以较小的惩罚参数实现所需的求解精度。还提出了求解非线性非线性PDE的数值方案。数值结果说明了理论发现，并证明了该方法的有效性和实用性。

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