A power penalty method for linear complementarity problems

Numerical performance of penalty method for American option pricing

“…Moreover, for the matrix I + (1 − θ)M , all the off-diagonal entries are negative and the diagonal entries are non-negative, by Lemma 2. Thus, under these two conditions, this theorem is just a consequence of Lemma 2.1 in ( [10]), which gives a convergence result for a more general linear complementarity problem.…”

“…Then, there exists a constant C > 0, independent of λ and k, such that This theorem is just a consequence of Theorem 2.1 in ( [10]) based on Theorem 3. We thus omit the proof of this theorem and refer the reader to ( [10]). …”

“…Though an analytical solution is available for the basic Black-Scholes equation, numerical methods still provide the most effective way for solving general Black-Scholes equations. American options are governed by a linear complementarity problem involving Black-Scholes operators ( [10,12]) which is much hard to solve then a single Black-Scholes equation. Thus, efficient and robust numerical methods are crucial for valuating American options, as will be seen later in this paper.…”

A feasible decomposition method for constrained equations and its application to complementarity problems

“…(s.2) Choose a working set Q j , find y j ∈ arg min y≥0 f j (y). Compute w j+1 according to (13). set j = j + 1, go to s.1.…”

Two SAOR Iterative Formats for Solving Linear Complementarity Problems

“…A large number of papers have studied LCP [3][4][5][6][7][8][9][10][11][12][13][14]. Numerical methods for LCP fall into two major categories: direct methods and iterative methods.…”