On convergence of a semi-analytical method for American option pricing

We examine the valuation of American put options by a semi-analytical method, and obtain the prior estimate and the convergence of the approximate solution. Our proofs are based on the embedding theorem in Sobolev space and the theory of functional analysis, in particular, the theory of weak compactness. The results in this paper theoretically confirm empirical observations that these methods are accurate and computationally efficient.