Variational and Quasi–Variational Inequalities: Applications to Control and Finance
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Beschreibung
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.
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.
Is comprehensive treatment of quasi–variational inequalities (QVIs) Presents direct integration with impulse control theory Provides strong emphasis on long-time behavior and asymptotic analysis
Autor*in
Salah Boulaaras
Themen in »Variational and Quasi–Variational Inequalities: Applications to Control and Finance«
Quasi-Variational Inequalities Impulse Control Problems State-Dependent Constraints American Option Pricing Free Boundary Problems Nonlinear Partial Differential Equations Asymptotic Stability and Long-Time Behavior Penalty Methods and Hemivariational Inequalities Finite Element Approximation Numerical Methods for Constrained Systems