@Article{NMTMA-2-202,
author = {},
title = {A Power Penalty Approach to Numerical Solutions of Two-Asset American Options},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2009},
volume = {2},
number = {2},
pages = {202--223},
abstract = {<p style="text-align: justify;">This paper aims to develop a power penalty method for a linear parabolic variational inequality (VI) in two spatial dimensions governing the two-asset American option valuation. This method yields a two-dimensional nonlinear parabolic PDE containing a power penalty term with penalty constant $\lambda &gt; 1$ and a power parameter $k&gt;0$. We show that the nonlinear PDE is uniquely solvable and the solution of the PDE converges to that of the VI at the rate of order $O( \lambda^{-k/2}) $. A fitted finite volume method is designed to solve the nonlinear PDE, and some numerical experiments are performed to illustrate the usefulness of this method.</p>},
issn = {2079-7338},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/nmtma/6022.html}
}