Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {M.~Holtz and A.~Kunoth},
  title = {{B-spline based monotone multigrid methods, with an
		  application to the pricing of American options}},
  booktitle = {Multigrid, Multilevel and Multiscale Methods},
  year = {2005},
  editor = {P. Wesseling and C.W. Oosterlee and P. Hemker},
  volume = {},
  number = {},
  series = {Proc. EMG},
  pages = {},
  address = {},
  month = {},
  organization = {},
  publisher = {},
  pdf = { 1},
  abstract = {We propose a monotone multigrid method based on a
		  B--spline basis of arbitrary smoothness for the efficient
		  numerical solution of elliptic variational inequalities on
		  closed convex sets. In order to maintain monotonicity
		  (upper bound) and quasi--optimality (lower bound) of the
		  coarse grid corrections, we propose coarse grid
		  approximations of the obstacle function which are based on
		  B--spline expansion coefficients. To illustrate the
		  potential of the scheme, the method is applied to the
		  pricing of American options in the Black--Scholes
  note = {Also as SFB 611 preprint No. 0289, 2006},
  annote = {article,ALM}