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 nonl...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 constantλ>1 and a power parameter k>0.We show that the nonlinear PDE is uniquely solvable and the solution of the PDE converges to that of theⅥat the rate of order(?)(λ^(-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.展开更多
文摘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 constantλ>1 and a power parameter k>0.We show that the nonlinear PDE is uniquely solvable and the solution of the PDE converges to that of theⅥat the rate of order(?)(λ^(-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.
