Black-Scholes Variational Inequalities

The effective numerical treatment of Black-Scholes equations is among the key issues in mathematical finance. The most important strategy for pricing American options relies on deterministic evolutionary variational inequalities on unbounded domains. This book provides the requisite mathematical background for the numerical treatment in weighted Sobolev spaces. The main focus is on the numerical analysis including a priori and a posteriori error estimates for finite element methods and the effective simulation based on the design of adaptive mesh refinement algorithms. Numerical experiments that illustrate the advantage of this approach conclude this book which is intended for graduate students and researchers in the area of mathematical finance and numerical analysis.