Stochastic variational inequalities: single-stage to multistage

Variational inequality modeling, analysis and computations are important for many applications, but most of the subject has been developed in a deterministic setting with no uncertainty in a problem’s data. In recent years research has proceeded on a track to incorporate stochasticity in one way or another. However, the main focus has been on a rather limited idea of what a stochastic variational inequality might be. Because variational inequalities are especially tuned to capturing conditions for optimality and equilibrium, stochastic variational inequalities ought to provide such service for problems of optimization and equilibrium in a stochastic setting. Therefore they ought to be able to deal with multistage decision processes involving actions that respond to increasing levels of information, which has so far hardly been the case. This can be accommodated by bringing in the tools of nonanticipativity and its martingale dualization, as shown here.