Variational Inequalities in Management Science and Finance

Springer Link

Authors: 

Andrianos E. Tsekrekos
Department of Accounting and Finance, Athens University of Economics and Business, Athens, Greece

Athanasios N. Yannacopoulos
Department of Statistics, Athens University of Economics and Business, Athens, Greece

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.