Modelling

This chapter introduces the concept of variational inequalities and its connections with optimization problems. Variational inequalities are motivated by three important problems in management science and finance: transportation networks, game theory, and optimal stopping with applications in American type and real options. Using the above three motivating examples, a detailed modelling approach is used to reduce these problems to relevant variational inequalities and thus introduce the concept in both finite and infinite dimensional settings, as well as their various alternative formulations.