@TechReport{	  it:2015-001,
  author	= {Victor Shcherbakov and Elisabeth Larsson},
  title		= {Radial Basis Function Partition of Unity Methods for
		  Pricing Vanilla Basket Options},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2015},
  number	= {2015-001},
  month		= jan,
  abstract	= {Mesh-free methods based on radial basis function (RBF)
		  approximation are widely used for solving PDE problems.
		  They are flexible with respect to the problem geometry and
		  highly accurate. A disadvantage of these methods is that
		  the linear system to be solved becomes dense for globally
		  supported RBFs. A remedy is to introduce localisation
		  techniques such as partition of unity (PU). RBF-PU methods
		  allow for significant sparsification of the linear system
		  and lower the computational effort. In this work we apply a
		  global RBF method as well as an RBF-PU method to problems
		  in option pricing. We consider one- and two-dimensional
		  vanilla options. In order to price American options we
		  employ a penalty approach. The RBF-PU method is competitive
		  with already existing methods and the results are promising
		  for extension to higher-dimensional problems.}
}