This book provides a rigorous introduction to the theory, computation, and applications of variational inequalities (VIs), with a focus on applications in management science and finance. It aims to bridge the gap between the abstract mathematical treatments of the subject and simplistic, non-rigorous approaches often used in financial economics or managerial literature.
Building on fundamental examples of concrete applications drawn from management science and finance, the book gradually develops the connection between optimal stopping problems and variational inequalities. It provides precise results on their derivation, solution properties, and their use to derive optimal policies in general frameworks of stochastic factors driving the state processes. Emphasis is also placed on the numerical treatment and approximation of VIs. All technical results are illustrated in detail for the characteristic problems presented at the beginning as motivating examples. It also offers a brief introduction to more advanced topics, including VIs for multi-scale problems and VIs related to optimal stopping problems under model uncertainty.
This book will be of interest to graduate students and researchers who wish for a quick, yet thorough introduction to the field. Practitioners who want to familiarise themselves with applications of VIs in management science and finance will also find this book useful.
Modelling.- Analysis.- Numerics.- Applications.
Andrianos E. Tsekrekos is a Professor of Financial Derivatives and Real Options at the Department of Accounting and Finance and Director of the Applied Finance Lab, Athens University of Economics and Business (AUEB), Greece. Before joining AUEB, he has working experience at Lancaster University and Durham Business School, UK. His research interests are in derivatives pricing, real options theory, stochastic and implied volatility models and real estate economics. His work has been published in well-established academic journals, in edited volumes, and in practitioner-oriented books.
Athanasios N. Yannacopoulos is Professor of Applied Stochastic Analysis at the Department of Statistics of the Athens University of Economics and Business (AUEB) Greece, and currently the Director of the Stochastic Modelling and Applications Research Laboratory (AUEB), and the MSc in Quantitative Methods in Actuarial and Financial Risk (AUEB). His research interests focus on stochastic and nonlinear analysis, uncertainty quantification, robust stochastic optimal control, and decision theory under uncertainty with special emphasis on economics and finance. His work has been published in well-established academic journals and is the co-author of a research monograph and an advanced textbook related to stochastic and nonlinear analysis.
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