Variational and Quasi-Variational Inequalities: Applications to Control and Finance

This book presents a rigorous and modern treatment of variational and quasi–variational inequalities, with applications to impulse control, nonlinear partial differential equations, and mathematical finance. It develops the theory of state-dependent constrained systems, where the admissible set depends on the unknown solution itself, leading to challenging nonlinear analytical structures. The book covers existence and stability theory, fixed-point methods, impulse control problems, asymptotic analysis, penalty techniques, and numerical approximation methods. Special attention is devoted to applications in optimal control and American option pricing. Combining functional analysis, nonlinear PDEs, optimization, and computational mathematics, this book offers a unified framework that bridges theoretical developments with practical modeling applications. Detailed numerical examples and computational approaches complement the analytical results. Designed for researchers, graduate students, and specialists in applied mathematics, control theory, numerical analysis, and financial mathematics, the book provides both advanced theoretical insight and practical tools for studying complex systems governed by state-dependent constraints.